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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces free real algebraic geometry; linear matrix inequality (LMI); semidefinite programming (SDP); noncommutative algebra inequalities Helton, J. W.; Klep, I.; Nelson, C. S., Noncommutative polynomials nonnegative on a variety intersect a convex set, J. Funct. Anal., 266, 6684-6752, (2014) Real algebra, Noncommutative algebraic geometry, Operator spaces and completely bounded maps, Semidefinite programming, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Semialgebraic sets and related spaces Noncommutative polynomials nonnegative on a variety intersect a convex set
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hecke algebras and their representations, Kac-Moody groups, Grassmannians, Schubert varieties, flag manifolds Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ring of differential operators on an affine algebraic variety Smith, S.P.: Differential operators on commutative algebras. (Lect. Notes Math. vol. 1197) Berlin Heidelberg New York: Springer 1986 Modules of differentials, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Singularities in algebraic geometry Differential operators on commutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces invariant Hilbert scheme; spherical variety; equivariant degeneration Papadakis, SA; Steirteghem, B, \textit{equivariant degenerations of spherical modules: part} II, Algebr. Represent. Theory, 19, 1135-1171, (2016) Compactifications; symmetric and spherical varieties, Fine and coarse moduli spaces, Parametrization (Chow and Hilbert schemes), Representation theory for linear algebraic groups Equivariant degenerations of spherical modules. II
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Rees algebras; blow up algebras; toric rings; special fiber rings; Ferrers graph; Koszul Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Toric varieties, Newton polyhedra, Okounkov bodies, Quadratic and Koszul algebras, Combinatorial aspects of commutative algebra, Combinatorial aspects of simplicial complexes Koszul blowup algebras associated to three-dimensional Ferrers diagrams
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Macdonald polynomials; current algebra; semi-infinite flag manifold Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Representation theory for linear algebraic groups, Symmetric functions and generalizations, Grassmannians, Schubert varieties, flag manifolds Representation theoretic realization of non-symmetric Macdonald polynomials at infinity
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hasse principle; simply connected symmetric space of a simple group Rapinchuk, A. S., The Hasse principle for symmetric spaces, Dokl. Akad. Nauk. BSSR, 31, 773-776, (1987) Homogeneous spaces and generalizations, Global ground fields in algebraic geometry, Linear algebraic groups over arbitrary fields The Hasse principle for symmetric spaces
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Chow group; Deligne cohomology; cycle map; product of two elliptic curves Esnault, H., Levine, M.: The Steinberg curve. Am. J. Math. 122(4), 783--804 (2000) Algebraic cycles, (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Symbols, presentations and stability of \(K_2\), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) The Steinberg curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cycle class map; Chow group; decomposable cycles; indecomposable cycles; product of three elliptic curves Gordon, B.B., Lewis, J.D.: Indecomposable higher Chow cycles. In: The Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998), vol. 548, pp. 193-224. Nato Science Series C: - Mathematical and Physical Sciences, vol. 548. Kluwer Academic Publication, Dordrecht (2000) Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles, Parametrization (Chow and Hilbert schemes), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Indecomposable higher Chow cycles
| 1 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Chow ring; constant cohomology ring; ring of formal power series; quantum cohomology; contact product; number of rational plane curves [EK2]Ernström, L. andKennedy, G., Contact cohomology of the projective plane,Amer. J. Math. 121 (1999), 73--96. Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Enumerative problems (combinatorial problems) in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Parametrization (Chow and Hilbert schemes) Contact cohomology of the projective plane
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Néron model; slit analytic space; Abel-Jacobi map; admissible normal function; variation of Hodge structure; limit mixed Hodge structure; motivic cohomology; unipotent monodromy; semistable reduction; algebraic cycle; higher Chow cycle; Ceresa cycle; Clemens-Schmid sequence; polarization; slit analytic space Green, Mark; Griffiths, Phillip; Kerr, Matt, Néron models and limits of Abel-Jacobi mappings, Compos. Math., 0010-437X, 146, 2, 288-366, (2010) Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Fibrations, degenerations in algebraic geometry, Variation of Hodge structures (algebro-geometric aspects), Motivic cohomology; motivic homotopy theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Néron models and limits of Abel-Jacobi mappings
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves proof of Quillen-Lichtenbaum conjecture for curves and surfaces; higher Chow groups; transfer homomorphisms; presheaf with transfers; Grothendieck topology; Nisnevich topology; triangulated category of motives; Tate motive; motivic cohomology; motivic Borel-Moore homology; sheaves of equidimensional cycles A. Suslin, Algebraic \(K\)-theory and Motivic Cohomology, Proc. International Congress of Mathematicians, Zürich 1994, vol. 1, Birkhäuser, 1995, pp. 342-351. \(K\)-theory in geometry, Generalizations (algebraic spaces, stacks), Étale and other Grothendieck topologies and (co)homologies, \(K\)-theory and homology; cyclic homology and cohomology Algebraic \(K\)-theory and motivic cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves value of L-series of elliptic curve; Deligne cohomology; Massey higher products; de Rham cohomology; dilogarithm \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Secondary and higher cohomology operations in algebraic topology, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) Higher order operations in Deligne cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Galois cohomology; Brauer group; Chow group; \(K\)-theory of a product of Severi-Brauer varieties; product of two conics Peyre, E., Products of Severi-Brauer varieties and Galois cohomology, (\textit{K}-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras, Santa Barbara, CA, 1992, Proc. Sympos. Pure Math., vol. 58, (1995), Amer. Math. Soc. Providence, RI), 369-401 Applications of methods of algebraic \(K\)-theory in algebraic geometry, Brauer groups of schemes, Galois cohomology, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Quadratic forms over general fields, Parametrization (Chow and Hilbert schemes) Products of Severi-Brauer varieties and Galois cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomology of hyperbolic three-manifolds; automorphic representations; holomorphic Siegel modular forms; \(l\)-adic representations; elliptic curves over imaginary quadratic fields; Tate module; Ramanujan conjecture; \(L\)-function Taylor, Richard, \textit{l}-adic representations associated to modular forms over imaginary quadratic fields. II, Invent. Math., 116, 1-3, 619-643, (1994) Representation-theoretic methods; automorphic representations over local and global fields, Congruences for modular and \(p\)-adic modular forms, Cohomology of arithmetic groups, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Other groups and their modular and automorphic forms (several variables), Elliptic curves over global fields, Galois representations, Local ground fields in algebraic geometry \(l\)-adic representations associated to modular forms over imaginary quadratic fields. II
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves existence of curves on abelian variety; product of two elliptic curves; degree of irrationality Yoshihara, H, Existence of curves of genus three on a product of two elliptic curves, J. Math. Soc. Japan, 49, 531-537, (1997) Special algebraic curves and curves of low genus, Elliptic curves, Abelian varieties and schemes Existence of curves of genus three on a product of two elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves mixed motive; algebraic \(K\)-theory of a scheme; Bloch-Ogus cohomology theory; motivic cohomology; triangulated tensor category; cycle formalism; motivic differential graded category; higher Chow groups; cycle class maps; \(K\)-theory; Chern classes; Riemann-Roch theorem; Chern character; Tannakian categories; triangulated Tate motivic category Marc Levine, Mixed motives, Mathematical Surveys and Monographs 57, American Mathematical Society, 1998 Generalizations (algebraic spaces, stacks), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Research exposition (monographs, survey articles) pertaining to \(K\)-theory, Algebraic cycles, (Equivariant) Chow groups and rings; motives, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Riemann-Roch theorems, Higher symbols, Milnor \(K\)-theory, \(K\)-theory of schemes, Relations of \(K\)-theory with cohomology theories, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Parametrization (Chow and Hilbert schemes), (Co)homology theory in algebraic geometry Mixed motives
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves two-dimensional topological quantum field theory; quantum cohomology; symplectic manifolds; algebraic curves; moduli of algebraic curves; higher-genus symplectic invariants; topological gravity Pandharipande R, Pixton A, Zvonkine D. Relations on \(\mathcal{M}\=\)\_{}\{g,n\} via 3-spin structures. ArXiv:1303.1043 Applications of global analysis to the sciences, Quantization in field theory; cohomological methods, Families, moduli of curves (algebraic), General geometric structures on manifolds (almost complex, almost product structures, etc.), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Model quantum field theories Higher genus symplectic invariants and sigma models coupled with gravity
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves finite field; product of elliptic curves; Tate conjecture; Chow motives; theory of Honda-Tate Spiess, M., Proof of the Tate conjecture for products of elliptic curves over finite fields, Math. Ann., 314, 285-290, (1999) Varieties over finite and local fields, Finite ground fields in algebraic geometry, Algebraic cycles, Elliptic curves over global fields, Elliptic curves, \(p\)-adic cohomology, crystalline cohomology Proof of the Tate conjecture for products of elliptic curves over finite fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves field of characteristic zero; integrable \(K\)-connection; smooth variety; characteristic classes; Chow group; cycle map in the Deligne cohomology Esnault, Hélène, Characteristic classes of flat bundles. II, \(K\)-Theory, 6, 1, 45-56, (1992) Characteristic classes and numbers in differential topology, Homology with local coefficients, equivariant cohomology, Étale and other Grothendieck topologies and (co)homologies Characteristic classes of flat bundles. II
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher Chow group; Shimura curves; modular families of Abelian surfaces; nullhomologous cycles; Heegner points on modular curves; CM cycle doi:10.1023/A:1017515926669 Algebraic cycles, (Equivariant) Chow groups and rings; motives, Arithmetic aspects of modular and Shimura varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Modular and Shimura varieties Relations among Heegner cycles on families of Abelian surfaces.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Beilinson conjectures; generalized regulators; Beilinson's motivic cohomology; higher Chow groups; generalized cycle maps; Eisenstein symbol; mixed motives; Deligne conjecture C. Deninger and A. Scholl, The Beilinson conjectures, \textit{L}-functions and arithmetic (Durham 1989), London Math. Soc. Lecture Note Ser. 153, Cambridge University Press, Cambridge (1991), 173-209. Varieties and morphisms, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic cycles The Beilinson conjectures
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve; hyperelliptic curve; curves of genus two or three; rational torsion subgroups; Jacobian varieties of curves Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn, Large torsion subgroups of split Jacobians of curves of genus two or three, Forum Math., 12, 3, 315-364, (2000) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for curves, Special algebraic curves and curves of low genus Large torsion subgroups of split Jacobians of curves of genus two or three
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves periods of an algebraic cycle; values of L-functions; higher regulators; Hodge conjecture; motives; Riemann-Roch theorem; multidimensional analog of Arakelov's construction of Néron-Tate height on curves; deformation of Chern classes; stable cohomology of current algebras Beilinson, A., Higher regulators and values of \textit{L}-functions, J. Sov. Math., 30, 2036-2070, (1985) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Higher regulators and values of \(L\)-functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of two elliptic curves; surface with a structure of a fiber space; degree of irrationality Yoshihara, H., \textit{degree of irrationality of a product of two elliptic curves}, Proc. Amer. Math. Soc., 124, 1371-1375, (1996) Special surfaces, Elliptic curves, Arithmetic theory of algebraic function fields Degree of irrationality of a product of two elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves with complex multiplication; curves of genus 2; Jacobians; product surfaces; abelian variety; Humbert invariant; binary and ternary quadratic forms; idoneal numbers; mass formula Kani, E., Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms, J. Number Theory, 139, 138-174, (2014) Elliptic curves over global fields, Abelian varieties of dimension \(> 1\), Complex multiplication and moduli of abelian varieties, Forms of degree higher than two, Jacobians, Prym varieties Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Kronecker series; \(L\)-functions of symmetric powers of elliptic curves; Beilinson's conjecture; motivic cohomology groups; Bloch-Beilinson regulator; de Rham cohomology Mestre, J. -F.; Schappacher, N.: Séries de Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q. Progr. math. 89, 209-245 (1991) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), (Co)homology theory in algebraic geometry Kronecker series and \(L\)-functions of symmetric powers of elliptic curves over \(\mathbb{Q}\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus two; Jacobians; rational torsion subgroup; elliptic curves; table of groups Leprévost, F.; Howe, E.; Poonen, B.: Sous-groupes de torsion d'ordres élevés de jacobiennes décomposables de courbes de genre 2 (Large torsion subgroups of split Jacobians of curves of genus 2). C. R. Acad. sci. Paris sér. I math. 323, 1031-1034 (1996) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\) Large torsion subgroups of split Jacobians of curves of genus 2
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves local intersection number of two curves; infinitely near points; intersection numbers; curve and its polar; duality; Schubert cycle Teissier, B.: Quelques points de l'histoire des variétés polaires, de Poncelet à nos jours, (1988) History of geometry, History of mathematics in the 19th century, History of mathematics in the 20th century, Questions of classical algebraic geometry, History of algebraic geometry Quelques points de l'histoire des variétés polaires, de Poncelet à nos jours. (Some points of the history of polarized varieties, from Poncelet till our days)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves stability of Picard bundle; Jacobian variety; theta divisor; semistability of higher conormal bundles for elliptic curves Ein, L.; Lazarsfeld, R., Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves, complex projective geometry, \textit{London Math. Soc. Lect. Note Ser.}, 179, 149-156, (1992) Jacobians, Prym varieties, Vector bundles on curves and their moduli Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves existence of higher logarithms; polylogarithm; dilogarithm; \(K\)-theory; Deligne-Beilinson cohomology; multivalued differential forms; Grassmann complex; higher Albanese manifolds; \(K(\pi,1)\)-spaces; 3-logarithm Hain (R.), MacPherson (R.).â Higher Logarithms, Ill. J. of Math,, vol. 34, N2, p. 392-475 (1990). Picard schemes, higher Jacobians, Grassmannians, Schubert varieties, flag manifolds, Applications of methods of algebraic \(K\)-theory in algebraic geometry Higher logarithms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves quartic residue; two dimensional irreducible complex representation; cusp form of weight one; Weil-Langlands theory; Fourier coefficients; identities between cusp forms; quartic reciprocity; higher reciprocity law; cusp form of weight two; inverse Mellin transform; L-function of elliptic curve; congruence mod 4 N. Ishii, ''Cusp forms of weight one, quadratic reciprocity and elliptic curves,''Nagoya Math. J.,98, 117--137 (1985). Holomorphic modular forms of integral weight, Congruences for modular and \(p\)-adic modular forms, Langlands-Weil conjectures, nonabelian class field theory, Elliptic curves Cusp forms of weight one, quartic reciprocity and elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves mixed Hodge structure; second cohomology group; Hessian family of elliptic curves Variation of Hodge structures (algebro-geometric aspects), Families, moduli of curves (algebraic), Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic topology on manifolds and differential topology, Elliptic curves A geometric example of non-trivially mixed Hodge structures
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; Chow ring; moduli space of stable curves; intersection product; Riemann-Roch theorem Mumford, D.: Towards an Enumerative Geometry of the Moduli Space of Curves, Arithmetic and Geometry, Vol. II, Progress in Mathematics, vol.~36, pp.~271-328. Birkhäuser Boston, Boston (1983) Families, moduli of curves (algebraic), Enumerative problems (combinatorial problems) in algebraic geometry, Parametrization (Chow and Hilbert schemes), Algebraic moduli problems, moduli of vector bundles, Fine and coarse moduli spaces, Riemann-Roch theorems Towards an enumerative geometry of the moduli space of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic modular forms; pairing; Hecke action; Serre-Tate invariant; forms of higher weight; integrality properties; de Rham cohomology; reduction properties; Igusa curve; crystalline cohomology; Galois representation Robert F. Coleman, A \?-adic inner product on elliptic modular forms, Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991) Perspect. Math., vol. 15, Academic Press, San Diego, CA, 1994, pp. 125 -- 151. \(p\)-adic theory, local fields, Galois representations, Arithmetic aspects of modular and Shimura varieties, \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Local ground fields in algebraic geometry A \(p\)-adic inner product on elliptic modular forms. -- Appendix: Forms on an annulus
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves tautological class; intersection product; moduli space of stable curves; generators for the Chow group; rank of the homology group Edidin, D, The codimension-two homology of the moduli space of stable curves is algebraic, Duke Math. J., 67, 241-272, (1992) Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes), Étale and other Grothendieck topologies and (co)homologies The codimension-two homology of the moduli space of stable curves is algebraic
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves torsion points of abelian varieties; product of non-isogenous elliptic curves [4] M. Hindry & N. Ratazzi, `` Torsion dans un produit de courbes elliptiques {'', \(J. Ramanujan Math. Soc.\)25 (2010), no. 1, p. 81-111. &MR 26 | &Zbl 1206.} Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties, Elliptic curves over global fields Torsion in a product of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher arithmetic Chow groups; arithmetic intersection theory; height pairing; Beilinson regulator; Deligne cohomology Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Heights Higher arithmetic intersection theory
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Abel-Jacobi map; regulator; Deligne cohomology; higher Chow group Kerr, Matt and Lewis, James D. and Müller-Stach, Stefan, The {A}bel--{J}acobi map for higher {C}how groups, Compositio Mathematica, 142, 2, 374-396, (2006) Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) The Abel-Jacobi map for higher Chow groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Jacobian of Hurwitz curve; decomposition of a Jacobian as product of elliptic curves Bennama, H.; Carbonne, P.: Périodes et jacobiennes des courbesxm+Ym+Zm=0. Bull. Polish acad. Sci. 44 (1996) Jacobians, Prym varieties, Theta functions and curves; Schottky problem, Picard schemes, higher Jacobians Periods and Jacobians of the curves \(X^ mY+Y^ mZ+Z^ mX=0\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Calabi-Yau threefolds; unipotent monodromy; variation of the Hodge structure; Picard-Fuchs differential equation; K3 surfaces; elliptic curves; product of a \(K3\) surface and an elliptic curve Garbagnati, A, New families of Calabi-Yau threefolds without maximal unipotent monodromy, Manuscripta Math., 140, 273-294, (2013) Calabi-Yau manifolds (algebro-geometric aspects), \(K3\) surfaces and Enriques surfaces, Mirror symmetry (algebro-geometric aspects), Structure of families (Picard-Lefschetz, monodromy, etc.), Variation of Hodge structures (algebro-geometric aspects), Families, moduli, classification: algebraic theory, Automorphisms of surfaces and higher-dimensional varieties New families of Calabi-Yau threefolds without maximal unipotent monodromy
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves transcendental numbers; simultaneous diophantine approximations to coordinates of points; product of elliptic curves; measure for algebraic independence; Weierstrass elliptic function Robert Tubbs, A Diophantine problem on elliptic curves, Trans. Amer. Math. Soc. 309 (1988), no. 1, 325 -- 338. Algebraic independence; Gel'fond's method, Elliptic curves A diophantine problem on elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli of curves; characteristic classes; torsors for elliptic curves; cohomology Taelman, L., Characteristic classes for curves of genus one, Michigan math. J., 64, 3, 633-654, (2015) Families, moduli of curves (algebraic), Elliptic curves Characteristic classes for curves of genus one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Deligne-Mumford compactification of the moduli space; curves of genus g; dimensions of the Chow groups Faber, C, Chow rings of moduli spaces of curves. I. the Chow ring of \(\overline{\mathcal M}_3\), Ann. Math. (2), 132, 331-419, (1990) Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes), Algebraic moduli problems, moduli of vector bundles Chow rings of moduli spaces of curves. I: The Chow ring of \(\bar {\mathcal M}_ 3\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cycle map; Chow ring; Deligne cohomology Esnault, Hélène; Levine, Marc: Surjectivity of cycle maps, Astérisque 218, 203-226 (1993) Algebraic cycles, Parametrization (Chow and Hilbert schemes), (Co)homology theory in algebraic geometry, Transcendental methods, Hodge theory (algebro-geometric aspects) Surjectivity of cycle maps
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Chern classes; Chow groups; family of curves; Euler characteristic; cycle-theoretic self-intersection; Swan conductor Families, moduli of curves (algebraic), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Topological properties in algebraic geometry, \(p\)-adic cohomology, crystalline cohomology Euler characteristics and Swan conductors
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves numerical classification; elliptic surfaces; singular fibers of pencils of curves; curves of genus three Kazuhiro Uematsu, Numerical classification of singular fibers in genus 3 pencils, J. Math. Kyoto Univ. 39 (1999), no. 4, 763 -- 782. Pencils, nets, webs in algebraic geometry, Special algebraic curves and curves of low genus, Fibrations, degenerations in algebraic geometry, Families, moduli of curves (algebraic), Elliptic surfaces, elliptic or Calabi-Yau fibrations, Special divisors on curves (gonality, Brill-Noether theory) Numerical classification of singular fibers in genus 3 pencils
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of elliptic curves; principally polarized abelian surfaces; Jacobians; family of curves Birkenhake, A family of abelian surfaces and curves of genus 4, Manuscripta Math. 85 pp 393-- (1994) Algebraic theory of abelian varieties, Jacobians, Prym varieties, Families, moduli of curves (algebraic) A family of abelian surfaces and curves of genus four
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves \(p\)-divisible group; modular elliptic curves; Galois representation; companion form; tame ramification; cuspidal eigenform; Kodaira-Spencer pairing; Serre-Tate pairing; Tate module of the Jacobian; de Rham cohomology of the Igusa curve Robert, F, Coleman and josé felipe voloch, companion forms and Kodaira-spencer theory, Invent. Math., 110, 263-281, (1992) Holomorphic modular forms of integral weight, Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, \(p\)-adic cohomology, crystalline cohomology, Elliptic curves, Formal groups, \(p\)-divisible groups Companion forms and Kodaira-Spencer theory
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves étale cohomology; crystalline cohomology; period map; Tate-module of a \(p\)-divisible group; differentials; elliptic curves CREW (R.) . - Universal extensions and p-adic periods of elliptic curves , Compositio Math., t. 73, 1990 , p. 107-119. Numdam | MR 91k:11045 | Zbl 0742.14013 \(p\)-adic cohomology, crystalline cohomology, Elliptic curves, Period matrices, variation of Hodge structure; degenerations, Arithmetic ground fields for curves, Étale and other Grothendieck topologies and (co)homologies, Formal groups, \(p\)-divisible groups Universal extensions and \(p\)-adic periods of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves unirational; uniruled; characteristic \(p\); moduli of curves; elliptic curves; modular forms; étale cohomology Rational and unirational varieties, Families, moduli of curves (algebraic) \(\overline M_{1,n}\) is usually not uniruled in characteristic \(p\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves zeta functions; distribution of zeros; \(L\)-functions; finite fields; automorphic \(L\)-functions; GUE measure; Montgomery-Odlyzko law; normalized spacings; Wigner measure; Kolmogoroff-Smirnov discrepancy function; generalized Sato-Tate conjecture; low-lying zeros; \(L\)-functions of elliptic curves; spacings of eigenvalues; Haar measure; Fredholm determinants; Deligne's equidistribution theorem; monodromy; Kloosterman sums N.M. Katz and P. Sarnak. \textit{Random matrices, Frobenius eigenvalues, and monodromy, vol. 45 of American Mathematical Society Colloquium Publications}. American Mathematical Society, Providence, RI (1999). Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, \(\zeta (s)\) and \(L(s, \chi)\), Analytic computations, Structure of families (Picard-Lefschetz, monodromy, etc.), Varieties over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Limit theorems in probability theory Random matrices, Frobenius eigenvalues, and monodromy
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomology of function field of a curve; complete discretely valued field; function ring of curves; existence of noncrossed product division algebras; function field of \(p\)-adic curve E. Brussel and E. Tengan, \textit{Formal constructions in the Brauer group of the function field of a p-adic curve}, Transactions of the American Mathematical Society, to appear. Brauer groups of schemes, Curves over finite and local fields, Brauer groups (algebraic aspects), Finite-dimensional division rings Formal constructions in the Brauer group of the function field of a \(p\)-adic curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves F-theory/heterotic string duality; Jacobian elliptic fibrations on \(K3\) surfaces; Kummer surfaces of genus-two curves Malmendier, A. and Shaska, T., The {S}atake sextic in {F}-theory, Journal of Geometry and Physics, 120, 290-305, (2017) Relationships between surfaces, higher-dimensional varieties, and physics, \(K3\) surfaces and Enriques surfaces, Modular and automorphic functions The Satake sextic in F-theory
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves abelian varieties of Kuga's type; zeta functions; absolute Hodge cycles; product of two Shimura curves Abdulali, S.: Zeta functions of Kuga fiber varieties. Duke Math. J.57, 333--345 (1988) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic theory of abelian varieties Zeta functions of Kuga fiber varieties
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves density of subvarieties; product of elliptic curves; moduli space; principally polarized abelian varieties; codimension E. Izadi, Density and completeness of subvarieties of moduli spaces of curves or abelian varieties, Math. Ann. 310 (1998), no. 2, 221 -- 233. Algebraic moduli problems, moduli of vector bundles, Algebraic moduli of abelian varieties, classification, Families, moduli of curves (algebraic), Elliptic curves Density and completeness of subvarieties of moduli spaces of curves or abelian varieties
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cup-product of two cohomology classes of holomorphic type; arithmetic quotient of a Hermitean symmetric space; Vogan-Zuckerman representations; vanishing theorems Clozel, L.: Produits dans la cohomologie holomorphe des variétés de Shimura II : Calculs et applications. J. reine angew. Math. 444, 1-15 (1993) Modular and Shimura varieties, Homogeneous spaces and generalizations, Classical real and complex (co)homology in algebraic geometry, Cohomology theory for linear algebraic groups Products in the holomorphic cohomology of Shimura varieties. II. Computations and applications
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Gazaki type filtration; higher Chow groups of zero cycles; Somekakawa type \(K\)-group; étale cycle map; reciprocity map Algebraic cycles, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Local ground fields in algebraic geometry, Abelian varieties of dimension \(> 1\) A filtration on the higher Chow group of zero cycles on an abelian variety
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Arakelov geometry; higher Chow groups; Beilinson regulator; intersection theory; Deligne cohomology José Ignacio Burgos Gil and Elisenda Feliu, Higher arithmetic Chow groups, Comment. Math. Helv. 87 (2012), no. 3, 521 -- 587. Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Higher arithmetic Chow groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher algebraic \(K\)-theory; higher Chow groups; bivariant cycle cohomology theory; Borel-Moore homology A. A. Suslin, ''Higher Chow groups and etale cohomology,'' in Cycles, Transfers, and Motivic Homology Theories, Princeton, NJ: Princeton Univ. Press, 2000, vol. 143, pp. 239-254. (Equivariant) Chow groups and rings; motives, Étale and other Grothendieck topologies and (co)homologies, Motivic cohomology; motivic homotopy theory, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Higher Chow groups and étale cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of elliptic curves; elliptic modular surface; resolving singularities; Picard-Fuchs equation; elliptic fibration Structure of families (Picard-Lefschetz, monodromy, etc.), Modular and Shimura varieties, Elliptic curves Picard-Fuchs equations for elliptic modular varieties
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; Davenport's inequality; Čech cohomology of sheaves; Weierstrass form Elliptic curves over global fields, Elliptic curves, Global ground fields in algebraic geometry The explicit calculation of Čech cohomology and an extension Davenport's inequality
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; cohomology; double ramification cycle; partial differential equations Families, moduli of curves (algebraic), Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) DR/DZ equivalence conjecture and tautological relations
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher reciprocity law; modular functions of weight one; elliptic curves; 2-torsion M. Koike, ''Higher reciprocity law, modular forms of weight 1, and elliptic curves,''Nagoya Math. J.,98, 109--115 (1985). Langlands-Weil conjectures, nonabelian class field theory, Holomorphic modular forms of integral weight, Galois representations, Algebraic functions and function fields in algebraic geometry Higher reciprocity law, modular forms of weight 1 and elliptic curves
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves virtual fundamental class; Deligne-Mumford stack; excess integral; tautological ring; equivariant Chow group; equivariant cohomology; Gromov-Witten invariant; moduli spaces; pointed curves; enumerative geometry; moduli stacks; localization Tom Graber & Rahul Pandharipande, ``Localization of virtual classes'', Invent. Math.135 (1999) no. 2, p. 487-518 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Group actions on varieties or schemes (quotients), Enumerative problems (combinatorial problems) in algebraic geometry Localization of virtual classes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves mixed Hodge modules of geometric origin; cycle map; Hodge conjectures; higher Chow groups; Bloch's conjecture Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles, Parametrization (Chow and Hilbert schemes) On the injectivity of cycle maps
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Euler product; arithmetic surface; Jacobian zeta function; modular curve; survey; Dirichlet series; L-series of elliptic curves; conjecture of Birch and Swinnerton-Dyer; Hasse-Weil conjecture; analytic continuation; functional equation; Shimura-Taniyama conjecture; Serre's conjecture; modular representations Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Other Dirichlet series and zeta functions L-series of elliptic curves: Results, conjectures and consequences
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves crystals; mass of polarizations; semistable family of curves; principal polarizations on a product of supersingular elliptic curves; Jacobian of a curve [5] T. Ekedahl, `` On supersingular curves and abelian varieties {'', \(Math. Scand.\)60 (1987), no. 2, p. 151-178. &MR 9 | &Zbl 0641.} \(p\)-adic cohomology, crystalline cohomology, Jacobians, Prym varieties, Arithmetic ground fields for abelian varieties, Arithmetic ground fields for curves On supersingular curves and abelian varieties
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves mirror symmetry; mirror map; complete intersection Calabi-Yau spaces; Picard-Fuchs equations; instanton corrected Yukawa couplings; topological oneloop partition function; higher dimensional moduli spaces; closed formulas; prepotential; Kä|hler moduli fields; singular ambient space; nonsigular weighted projective spaces; three generation models; topology change; local solutions; topological invariants; Calabi-Yau manifold; rational superconformal field theories; elliptic curves; \(E_6\) gauge couplings; \(E_8\) gauge couplings; threshold corrections; Gromov-Witten invariants S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, \textit{Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces}, \textit{Nucl. Phys.}\textbf{B 433} (1995) 501 [hep-th/9406055] [INSPIRE]. Applications of deformations of analytic structures to the sciences, Calabi-Yau manifolds (algebro-geometric aspects), String and superstring theories; other extended objects (e.g., branes) in quantum field theory Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves p-adic L-function; Tate-module of an elliptic curve; Iwasawa-modules; CM- curves; two variable main conjecture Coates, J.; Schmidt, C.-G., Iwasawa theory for the symmetric square of an elliptic curve, Journal für die Reine und Angewandte Mathematik, 375/376, 104-156, (1987) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves Iwasawa theory for the symmetric square of an elliptic curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus two; elliptic curves; torsion points; Galois representations Boxall, J., Grant D.: Examples of torsion points on genus two curves. Trans. Am. Math. Soc. 352, 4533--4555 (2000) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry Examples of torsion points on genus two curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves in the unstable range; projective curves of higher genus; moduli space; cohomology; principally polarized Abelian varieties Cohomology of arithmetic groups, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic varieties and schemes; Arakelov theory; heights, Families, moduli of curves (algebraic) Virtual cohomology of the moduli space of curves in the unstable range
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher dimensional analogues of Brauer-Siegel theorem; constant families of elliptic curves and abelian varieties; gap in proof of main theorem Varieties over finite and local fields, Finite ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations Brauer-Siegel theorem for elliptic surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of elliptic curves; abelian surface Ruppert W.: When is an abelian surface isomorphic or isogenous to a product of elliptic curves?. Math. Z. 203, 293--299 (1990) Algebraic theory of abelian varieties, Isogeny, Elliptic curves When is an abelian surface isomorphic or isogenous to a product of elliptic curves?
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves polarized variations of the Hodge structures; Calabi-Yau families; family of elliptic curves; motivic mixed Hodge structure; Calabi-Yau three-folds Deligne, P.: \textit{Local behavior of Hodge structures at infinity}. In: Mirror symmetry, II. AMS/IP Stud. Adv. Math., Vol. 1, Providence, RI: Amer. Math. Soc., 1997, pp. 683-699 Variation of Hodge structures (algebro-geometric aspects), Calabi-Yau manifolds (algebro-geometric aspects), Enumerative problems (combinatorial problems) in algebraic geometry, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Local behavior of Hodge structures at infinity
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of sums of squares; Hopf condition; projective quadric; motivic cohomology; Chow group Dugger, D., Isaksen D.: The Hopf condition for bilinear forms over arbitrary fields. Ann. Math (2) 165, 943-964 (2007) Sums of squares and representations by other particular quadratic forms, Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) The Hopf condition for bilinear forms over arbitrary fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves arrangements of hyperplanes; cohomology of local systems on quasi-projective varieties; Orlik-Solomon algebras; complements to algebraic curves; complements to hyperplane arrangements; arrangements of lines in \(\mathbb P^2\); Deligne cohomology; Alexander invariants of plane algebraic curves; characteristic varieties A. Libgober and S. Yuzvinsky, ''Cohomology of local systems,'' in Arrangements--Tokyo 1998, Vol. 27 of Adv. Stud. Pure Math., Kinokuniya, Tokyo, 2000, pp. 169--184. Relations with arrangements of hyperplanes, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Analytic sheaves and cohomology groups, Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) Cohomology of local systems
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves genus; Jacobian; isogenous to a product of elliptic curves Torsten Ekedahl and Jean-Pierre Serre, Exemples de courbes algébriques à jacobienne complètement décomposable, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 5, 509 -- 513 (French, with English and French summaries). Jacobians, Prym varieties Examples of algebraic curves with totally split Jacobian
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher algebraic \(K\)-theory; Milnor \(K\)-theory; finite fields; Tate's conjecture; Beilinson's conjecture; Parshin's conjecture; Chow groups; category of pure motives; étale cohomology; motivic cohomology Thomas Geisser, ``Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\).'', \(K\)-Theory13 (1998) no. 2, p. 109-122 \(K\)-theory of schemes, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves bound on torsion of elliptic curves; symmetric product of modular curves; Eisenstein quotient; Hecke operators; Jacobian of \(X_ 0\); Hecke operator Kamienny, S., Torsion points on elliptic curves and \(q\)-coefficients of modular forms, Invent. Math., 109, 221-229, (1992) Elliptic curves, Modular and Shimura varieties, Elliptic curves over global fields, Jacobians, Prym varieties Torsion points on elliptic curves and \(q\)-coefficients of modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves glueing theorems; four-manifolds with boundary; smooth, oriented, closed four-manifold; Donaldson invariants; relative invariants; Floer homology; complex Kähler surface; normal-crossings surface; elliptic surfaces; quantum cohomology product; cohomology of the moduli space for stable vector-bundles S. K. Donaldson, Floer homology and algebraic geometry, Vector bundles in algebraic geometry (Durham, 1993) London Math. Soc. Lecture Note Ser., vol. 208, Cambridge Univ. Press, Cambridge, 1995, pp. 119 -- 138. Applications of global analysis to structures on manifolds, Special surfaces, Topological properties in algebraic geometry Floer homology and algebraic geometry
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves regulator map; Deligne-Beilinson cohomology; L-function of an elliptic curve with complex multiplication; Hecke L-function Christopher Deninger and Kay Wingberg, On the Beĭlinson conjectures for elliptic curves with complex multiplication, Beĭlinson's conjectures on special values of \?-functions, Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 249 -- 272. Applications of methods of algebraic \(K\)-theory in algebraic geometry, Complex multiplication and abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves, Generalizations (algebraic spaces, stacks) On the Beilinson conjectures for elliptic curves with complex multiplication
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus two; elliptic curves; elliptic differential Kani E.(1997). The existence of curves of genus 2 with elliptic differentials. J. Number Theory 64, 130--161 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves The existence of curves of genus two with elliptic differentials
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomology of algebraic curves; smooth irreducible curve; indecomposable \(F_ i[\Gamma ]\)-modules; moduli space; complex elliptic curves; decomposition formula; genus; number of cusps Chad Schoen, On certain modular representations in the cohomology of algebraic curves, J. Algebra 135 (1990), no. 1, 1 -- 18. Cohomology theory for linear algebraic groups, Étale and other Grothendieck topologies and (co)homologies, Elliptic curves, Representations of finite groups of Lie type, Representation theory for linear algebraic groups On certain modular representations in the cohomology of algebraic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves graded rings; Artin-Schelter regular algebras of global dimension three; noncommutative projective geometry; elliptic algebras; point modules; Noetherian domains; Hilbert series; elliptic curves -, Algebras associated to elliptic curves , Trans. Amer. Math. Soc. 349 (1997), 2317--2340. JSTOR: Graded rings and modules (associative rings and algebras), Elliptic curves, Noetherian rings and modules (associative rings and algebras), Homological dimension in associative algebras, Noncommutative algebraic geometry, Ordinary and skew polynomial rings and semigroup rings Algebras associated to elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves principally polarized abelian varieties; product of elliptic curves; modular curve \beginbarticle \bauthor\binitsV. \bsnmGonzález-Aguilera and \bauthor\binitsR. \bsnmRodríguez, \batitleFamilies of irreducible principally polarized Abelian varieties isomorphic to a product of elliptic curves, \bjtitleProc. Amer. Math. Soc. \bvolume128 (\byear2000), no. \bissue3, page 629-\blpage636. \endbarticle \OrigBibText V. González-Aguilera and R. Rodríguez. Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. Proceedings of the AMS , 128(3):629-636, 2000. \endOrigBibText \bptokstructpyb \endbibitem Algebraic theory of abelian varieties, Jacobians, Prym varieties, Elliptic curves Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve; tropical curve; tropical variety; intersection product; moduli space of curves Kerber, M.; Markwig, H., Counting tropical elliptic plane curves with fixed \textit{j}-invariant, Comment. Math. Helv., 84, 2, 387-427, (2009) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Polyhedra and polytopes; regular figures, division of spaces, Enumerative problems (combinatorial problems) in algebraic geometry Counting tropical elliptic plane curves with fixed \(j\)-invariant
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; conjectures of Birch and Swinnerton-Dyer; Euler product Stephens, N. M.: Conjectures concerning elliptic curves. Bull. Amer. Math. Soc.73, 160--163 (1967). \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Elliptic curves Conjectures concerning elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher genus Riemann surfaces; Deligne cohomology class; Earle-Eells fibration; Teichmüller space; Schwarzian cocycle; Hubbard's universal family of projective structures Aldrovandi, E; Takhtajan, L A, No article title, Commun. Math. Phys., 227, 303-348, (2002) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Applications of deformations of analytic structures to the sciences, Quantization in field theory; cohomological methods, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Operator algebra methods applied to problems in quantum theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Generating functional in CFT on Riemann surfaces II: Homological aspects
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves complete intersection of two quadrics; cohomology of the Fano 4-fold; Calabi-Yau 3-fold; cone of effective curves; extremal rays C. Borcea, \textit{Homogeneous vector bundles and families of Calabi-Yau threefolds. II}, \textit{Proc. Symp. Pure Math.}\textbf{52} (1991), with appendix by J. Kollár. \(3\)-folds, Fano varieties Homogeneous vector bundles and families of Calabi-Yau threefolds. II
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves lattices and their invariants; associated tori; elliptic functions; modular forms of one variable; periodic meromorphic functions; field of elliptic functions; Weierstrass \(\wp\)-function; elliptic curves; product representations; complex multiplication; Jacobi's theta series; Jacobi forms; modular functions; Siegel modular group; discontinuous subgroups; weight formula; Dedekind's eta-function; cusp forms; algebra of Hecke operators; Petersson inner product; Eisenstein series; Dirichlet series; functional equation; Hecke operators; harmonic polynomials; quadratic forms; Epstein zeta-function; Kronecker's limit formula; Rankin convolution M. Koecher and A. Krieg, \textit{Elliptische Funktionen und Modulformen}, Springer, Berlin, Heidelberg, 1998. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Holomorphic modular forms of integral weight, Elliptic functions and integrals, Elliptic curves, Hecke-Petersson operators, differential operators (one variable), Complex multiplication and moduli of abelian varieties, Theta series; Weil representation; theta correspondences, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Elliptic curves over global fields Elliptic functions and modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves constructible sheaf; cohomology of curves; Poincaré duality; proof of Weil conjecture; base change; Lefschetz trace formula; cycle map; rationality of L-series Milne, J. S.: Étale Cohomology. Princeton Univ. Press (1980) Étale and other Grothendieck topologies and (co)homologies, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Local structure of morphisms in algebraic geometry: étale, flat, etc., Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic problems in algebraic geometry; Diophantine geometry Étale cohomology. (Ehtal'nye kogomologii). Transl. from the English
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves high rank elliptic curves; nontrivial rational point of order two Kihara S., Proc. Japan Acad. Ser. A Math. Sci. 73 (9) pp 165-- (1997) Elliptic curves over global fields, Elliptic curves, Rational points Construction of high-rank elliptic curves with a non-trivial rational point of order 2
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher Chow groups; Beilinson's motivic cohomology; cycle class map; mixed motives Applications of methods of algebraic \(K\)-theory in algebraic geometry, Parametrization (Chow and Hilbert schemes), Generalizations (algebraic spaces, stacks), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols Extensions of motives, higher Chow groups and special values of \(L\)- functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves divided Frobenius; super-elliptic curves; Hasse-Witt matrix; Deligne-Illusie morphism; de Rham cohomology; crystalline cohomology de Rham cohomology and algebraic geometry, Integral representations, \(p\)-adic cohomology, crystalline cohomology Computation of the divided Frobenius modulo \(p\) on the crystalline cohomology of certain covers of the projective line
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves abelian surfaces; product of elliptic curves; Picard number Algebraic theory of abelian varieties, Special surfaces A note on non-simple abelian surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves zeta functions of elliptic curves; p-adic cohomology theories; number of points Landsburg, S. E.: P-adic cohomology and zeta functions of elliptic curves, queens papers in pure mathematics. (1986) Finite ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(p\)-adic cohomology, crystalline cohomology, Elliptic curves p-adic cohomology and zeta functions of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Mumford curve; Chow group; cycle map; Brauer group; Brauer-Manin pairing; Milnor K-group; Galois cohomology; semi-abelian variety; Tate elliptic curve Yamazaki T. (2005). On Chow and Brauer groups of a product of Mumford curves. Math. Ann. 333(3): 549--567 (Equivariant) Chow groups and rings; motives, Varieties over finite and local fields, Local ground fields in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) On Chow and Brauer groups of a product of Mumford curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves product of curves; cyclic quotient singularity; rational singularity; wild; intersection matrix; resolution graph; fundamental cycle Lorenzini, D.: Wild quotients of products of curves (2012, preprint) Singularities in algebraic geometry, Local ground fields in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of curves, local rings, Multiplicity theory and related topics, Singularities of surfaces or higher-dimensional varieties Wild quotients of products of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Hartshorne-Rao module; space curve; deficiency module; first cohomology of the ideal sheaf; number of minimal generators; two-codimensional subschemes of projective space; 1-Buchsbaum curves Migliore, J.: Submodules of the deficiency module. J. London math. Soc. (2) 48, 396-414 (1993) Low codimension problems in algebraic geometry, Plane and space curves, (Co)homology theory in algebraic geometry, Linkage Submodules of the deficiency module
| 0 |
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