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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-hyperelliptic curves; n-th symmetric product of curve; Jacobian; asymptotic direction Special algebraic curves and curves of low genus, Jacobians, Prym varieties, Elliptic curves On a characterization of elliptic-hyperelliptic 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 semistable curve; moduli of curves; resolution of singularities; alteration; integral variety; monoidal transformations; semi-stable reduction theorem; multiplicity of intersection for two modules; Monsky-Washnitzer cohomology groups; monodromy actions on étale cohomology Berthelot, P., Altérations de variétés algébriques (d'après A.J. de jong), Séminaire Bourbaki, vol. 1995/96, Astérisque, 241, 273-311, (1997), Exp. No. 815, 5 Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry, Families, moduli of curves (algebraic), \(p\)-adic cohomology, crystalline cohomology, Étale and other Grothendieck topologies and (co)homologies Alterations of algebraic varieties (after A. J. de Jong)
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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 torsion cycle map; Chow group of cycles of codimension two; Hochschild-Serre spectral sequence K. Sato, Injectivity of the torsion cycle map of codimension two of varieties over \(p\)-adic fields with semi-stable reduction , J. Reine Angew. Math. 501 (1998), 221--235. Algebraic cycles, Local ground fields in algebraic geometry, Parametrization (Chow and Hilbert schemes) Injectivity of the torsion cycle map of codimension two of varieties over \(p\)-adic fields with semi-stable reduction
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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 Seshadri constant; abelian varieties; product of elliptic curves; Gauss map; linear series DOI: 10.1353/ajm.1996.0028 Algebraic moduli of abelian varieties, classification, Divisors, linear systems, invertible sheaves, Elliptic curves Seshadri constants on 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 direct product of elliptic curves; Hodge conjecture; abelian variety Analytic theory of abelian varieties; abelian integrals and differentials, Transcendental methods, Hodge theory (algebro-geometric aspects), Special algebraic curves and curves of low genus, Elliptic curves Rational cycles on abelian varieties. 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 \(L\)-functions of varieties over global fields; elliptic curves; complex multiplication; polylogarithms; algebraic \(K\)-theory; Bloch-Kato conjecture; \(p\)-adic cohomology G. Kings, The Tamagawa number conjecture for CM elliptic curves , Invent. Math. 143 (2001), 571--627. \CMP1 817 645 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Polylogarithms and relations with \(K\)-theory, Abelian varieties of dimension \(> 1\), Complex multiplication and moduli of abelian varieties, \(p\)-adic cohomology, crystalline cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) The Tamagawa number conjecture for CM 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 regular mappings to spheres; algebraic approximation of mappings; product of real elliptic curves; real algebraic sets Bochnak J., Kucharz W.: Elliptic curves and real algebraic morphisms. J. Algebraic Geom. 2, 635--666 (1993) Real algebraic sets, Elliptic curves, Rational and birational maps Elliptic curves and real algebraic morphisms
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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 Bloch Beilinson conjecture; Hodge theory; variations of Hodge structure; variations of complex structure; period mappings; cohomology classes of an analytic cycle; algebraic cycles; mixed Hodge structures; infinitesimal variations of the Hodge structure; Abel-Jacobi map; Chow groups Voisin, C., Théorie de Hodge et géométrie algébrique complexe, (2002), Société mathématique de France Paris, Cours spécialisés Transcendental methods, Hodge theory (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Transcendental methods of algebraic geometry (complex-analytic aspects), Variation of Hodge structures (algebro-geometric aspects), Algebraic cycles, Period matrices, variation of Hodge structure; degenerations, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces Hodge theory and complex 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 Revolution surfaces of \(2^nd\) degree; conditions; equation of \(2^nd\) degree with three variables; axis; equator; product of two variables Surfaces in Euclidean and related spaces, Equations in general fields, Euclidean analytic geometry, Relational systems, laws of composition, Special surfaces General theory on the revolution surfaces of \(2^nd\) degree.
| 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 arithmetic Chow ring; Green currents; intersection of cycles; Deligne-Beilinson cohomology [8] Burgos~Gil (J.~I.).-- Arithmetic Chow rings and Deligne-Beilinson cohomology, J. Alg. Geom. 6 (1997), 335-377. &MR~14 | &Zbl~0922. Parametrization (Chow and Hilbert schemes), Algebraic cycles, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies Arithmetic Chow rings and Deligne-Beilinson cohomology
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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 Chow cycle; family of quartics; higher Chow group; singular Kummer surface (Equivariant) Chow groups and rings; motives, Algebraic cycles, Families, moduli, classification: algebraic theory, \(K3\) surfaces and Enriques surfaces, Motivic cohomology; motivic homotopy theory Indecomposable cycles on special quartics in \(\mathbb P^3\)
| 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 torsion points of elliptic curves; Iwasawa theory; Galois cohomology; maximal p-extension; \({bbfZ}_ p\)-extension; Galois groups; free pro-p- groups K. Wingberg , Galois groups of number fields generated by torsion points of elliptic curves . Nagoya Math. J 104 ( 1986 ), 43 - 53 . Article | MR 868436 | Zbl 0621.12011 Galois theory, Cyclotomic extensions, Elliptic curves, Galois cohomology, Ramification and extension theory, Global ground fields in algebraic geometry Galois groups of number fields generated by torsion points of 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 moduli spaces of stable curves; Deligne-Mumford moduli spaces; Gromov-Witten invariants; toric variety; quantum cohomology Spielberg, Holger, A formula for the {G}romov--{W}itten invariants of toric varieties, (None) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Toric varieties, Newton polyhedra, Okounkov bodies, Fano varieties A formula for the Gromov-Witten invariants of toric 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 three parameter family of elliptic curves; Mordell-Weil rank four; Prym varieties F. Hazama, Rational points on certain abelian varieties over function fields,J. Number Theory 50 (1995), 278--285. Elliptic curves, Picard schemes, higher Jacobians Rational points on certain abelian varieties over function fields
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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 variety; positive characteristic; product of supersingular elliptic curves; Frobenius; principal polarization T. Ibukiyama and T. Katsura: On the field of definition of superspecial polarized abelian varieties and type numbers, Compositio Math. 91 (1994), 37--46. Arithmetic ground fields for abelian varieties, Elliptic curves, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Relevant commutative algebra On the field of definition of superspecial polarized abelian varieties and type numbers
| 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 characteristics; (commutative and noncommutative) compact \(p\)-adic Lie groups; cohomology groups; special values of \(L\)-functions; elliptic curves; Iwasawa algebra R. Sujatha, Euler-Poincare characteristics of \(p\)-adic Lie groups and arithmetic, preprint, 2000. Representations of Lie and linear algebraic groups over local fields, Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves Euler-Poincaré characteristics of \(p\)-adic Lie groups and arithmetic
| 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 product; moduli spaces of curves; line bundles Families, moduli of curves (algebraic) Deligne products of line bundles over moduli spaces of 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 family of elliptic curves; motivic cohomology Wildeshaus, J., On an elliptic analogue of zagier's conjecture, Duke Math. J., 87, 2, 355-407, (1997) Generalizations (algebraic spaces, stacks), Elliptic curves, Elliptic curves over global fields, Relations of \(K\)-theory with cohomology theories, (Co)homology theory in algebraic geometry On an elliptic analogue of Zagier's conjecture
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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 hyperbolic three-manifolds; deformation of hyperbolic structures; Neumann-Zagier potential, Chern-Simons invariant; Deligne cohomology; variation of mixed Hodge structures. Eta-invariants, Chern-Simons invariants, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Chern-Simons variations and 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 higher weight cycles; modular forms of Nebentypus; intersection multiplicities of cycles; Hirzebruch-Zagier cycle; quaternionic modular surface; elliptic modular form B. Brent Gordon, Intersections of higher-weight cycles over quaternionic modular surfaces and modular forms of Nebentypus, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 293 -- 298. Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Local ground fields in algebraic geometry Intersections of higher-weight cycles over quaternionic modular surfaces and modular forms of Nebentypus
| 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 arithmetic curves; algebraic \(K\)-theory; polylogarithms; mixed Tate-Hodge structures; motivic cohomology; Deligne cohomology; Tannaka categories; cohomology of Lie algebras Motivic cohomology; motivic homotopy theory, Arithmetic ground fields for curves, Polylogarithms and relations with \(K\)-theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) An extension of Zagier's conjecture to a conjecture for 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 symmetric product of Riemann surfaces; Jacobian; Abel-Jacobi map; higher cohomology groups Lazarsfeld, R., Cohomology on symmetric products, syzygies of canonical curves, and a theorem of kempf, No. 145, 89-97, (1993) Riemann surfaces; Weierstrass points; gap sequences, Jacobians, Prym varieties, Classical real and complex (co)homology in algebraic geometry, Compact Riemann surfaces and uniformization Cohomology on symmetric products, syzygies of canonical curves, and a theorem of Kempf
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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 Dedekind ring; central simple algebra; hereditary R-order; Grothendieck group; finitely generated locally free \(\Lambda\)-modules; class group; finiteness theorems; affine k-algebra; Chow group; 0-dimensional cycles; conic bundle surface; sheaves of orders; Galois cohomology; global sections; Quillen resolution; Severi-Brauer schemes; reduced norm; Merkur'ev-Suslin theorems; cup-product; coordinate ring; smooth affine curve Salberger, P.:K-theory of orders and their Brauer-Severi schemes. Thesis, Department of Mathematics, University of G?teborg 1985 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Grothendieck groups, \(K\)-theory, etc., Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Finite rings and finite-dimensional associative algebras, Algebraic cycles, \(K\)-theory of global fields, Parametrization (Chow and Hilbert schemes), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Galois cohomology Galois descent and class groups of orders
| 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 space; Chow variety; \(n\)-convexity; ample normal bundle; topological space of compact \(n\)-cycles; analytic families of cycles; reduction of convexity; Cartier divisor; higher integration maps Barlet, D.: How to use the cycle cpace in complex geometry. Several Complex Variables MSRI Publications, vol. 37, pp. 25--42, 1999 Integration on analytic sets and spaces, currents, Divisors, linear systems, invertible sheaves, Foliations in differential topology; geometric theory How to use the cycle space in complex geometry
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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 polarization; characteristic p; Jacobian variety; supersingular elliptic curves; prescribed automorphism group; curves of genus two; Hasse-Witt- matrix; class numbers of quaternionic algebras T.IBUKIYAMA, T.KATSURA, and F.OORT,\textit{Supersingular curves of genus two and class numbers}, Compositio Math. 57 (1986), no. 2, 127--152.MR827350 Jacobians, Prym varieties, Quaternion and other division algebras: arithmetic, zeta functions, Finite ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Group actions on varieties or schemes (quotients), Families, moduli of curves (algebraic) Supersingular curves of genus two and class numbers
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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 stable vector bundle; higher rank Brill-Noether theory; Petri map; general curve; chain of elliptic curves; stable vector bundles on curves. A. Castorena, A. López Martín, M. Teixidor i Bigas, Petri map for vector bundles near good bundles. Special divisors on curves (gonality, Brill-Noether theory), Vector bundles on curves and their moduli Petri map for vector bundles near good bundles
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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 Calabi-Yau variety; algebraic cycle; Abel-Jacobi map; regulator; Deligne cohomology; Chow group Lewis, J. D.: Transcendental methods in the study of algebraic cycles with a special emphasis on Calabi-Yau varieties. In: Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds. Fields Institute Communications, vol. 67, 29-69, Springer, New York (2013) Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Calabi-Yau manifolds (algebro-geometric aspects), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Transcendental methods in the study of algebraic cycles with a special emphasis on Calabi-Yau 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 complete intersection of two plane curves; Hilbert function of a \(0\)- cycle D. S. Sodhi, ``Ice-induced vibrations of structures,'' Special Report 89-5, International Association for Hydraulic Research Working Group on Ice Forces, 1989. Complete intersections, Algebraic cycles, Enumerative problems (combinatorial problems) in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) A note on the intersection of a hypersurface with a finite set of points in \(\mathbb{P}^ n\)
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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 geometric approach to Eichler's arithmetic theory of definite quaternion algebras; modular forms of weight 3/2; Waldspurger's formula; elliptic curves with prime conductor; critical values of L-series; weight two cusp form; special points; height pairing B. H. Gross, ''Heights and the special values of \(L\)-series,'' in Number Theory, Providence, RI: Amer. Math. Soc., 1987, vol. 7, pp. 115-187. Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, Quaternion and other division algebras: arithmetic, zeta functions, Holomorphic modular forms of integral weight, Elliptic curves Heights and the special values of \(L\)-series
| 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 characteristic \(p\); Jacobian of a hyperelliptic curve; product of supersingular elliptic curves; genus; zero Hasse-Witt matrix Valentini, R., Hyperelliptic curves with zero Hasse-Witt matrix, Manuscr. Math., 86, 2, 185-194, (1995) Elliptic curves, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Hyperelliptic curves with zero Hasse-Witt matrix
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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 curves; Stark conjectures; conjecture of Birch and Swinnerton-Dyer; symbols; algebraic K-theory; algebraic geometry; Galois cohomology; group schemes; abelian varieties History of number theory, History of algebraic geometry, Collected or selected works; reprintings or translations of classics, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic problems in algebraic geometry; Diophantine geometry, Abelian varieties and schemes Collected works of John Tate. Part II (1976--2006). Edited by Barry Mazur and Jean-Pierre Serre
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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 product of two nonsingular projective curves defined over a finite field; order of the Brauer group; Artin-Tate formula; Artin-Mazur conjecture N. Yui, The arithmetic of the product of two Fermat curves over a finite field, preprint. Curves in algebraic geometry, Brauer groups of schemes, Finite ground fields in algebraic geometry, Arithmetic ground fields for curves The arithmetic of the product of two algebraic curves over a finite field
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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 logarithmic geometry; moduli of elliptic curves; elliptic cohomology; topological \(q\)-expansion; Witten genus; derived structure sheaf M. Hill T. Lawson Topological modular forms with level structure Elliptic cohomology, Stacks and moduli problems, Stable homotopy theory, spectra, Holomorphic modular forms of integral weight Topological modular forms with level structure
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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 biextensions; higher Chow groups; algebraic cycles; incidence equivalence; Poincaré biextension; Abel-Jacobi map; Deligne-Beilinson cohomology; torsors; Griffiths' conjecture S. Müller-Stach, \(\mathbb{C}^{*}\)-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles , \(K\)-Theory 9 (1995), 395-406. Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Algebraic cycles \(\mathbb{C}^*\)-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles
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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 compatibility for products; cohomology theories; Bloch's higher Chow groups; bivariant cycle cohomology; motivic cohomology; étale cohomology Weibel C. , Products in higher Chow groups and motivic cohomology , in: Algebraic K -theory (Seattle, WA, 1997) , Proceedings of Symposia in Pure Math. , 67 , 1999 , pp. 305 - 315 . MR 1743246 | Zbl 0942.19003 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Motivic cohomology; motivic homotopy theory, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Relations of \(K\)-theory with cohomology theories, \(K\)-theory and homology; cyclic homology and cohomology Products in higher Chow groups and motivic cohomology
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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; cycle map; Deligne-Beilinson cohomology; intermediate cohomology theory Esnault H. (1990). A note on the cycle map. J. Reine Angew. Math. 411: 51--65 (Co)homology theory in algebraic geometry, Parametrization (Chow and Hilbert schemes), Algebraic cycles A note on the cycle map
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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 \(K3\) surface; Legendre family of elliptic curves; mirror map; periods; Deligne's periods Mirror symmetry (algebro-geometric aspects), \(K3\) surfaces and Enriques surfaces \(K3\) mirror symmetry, Legendre family and Deligne's conjecture for the Fermat quartic
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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 moduli space of curves; Chow ring; tautological classes; algebraic cohomology ring; hard Lefschetz property; Hodge positivity property Faber, C., \textit{A conjectural description of the tautological ring of the moduli space of curves}, Moduli of curves and abelian varieties, 109-129, (1999), Vieweg, Braunschweig Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes), (Equivariant) Chow groups and rings; motives, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry A conjectural description of the tautological ring of the moduli space of 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 currents; Deligne cohomology; regulator; Abel-Jacobi map; higher Chow group Kerr, M., Lewis, J.D., Lopatto, P.: Simplicial Abel-Jacobi maps and reciprocity laws, preprint (2015). arXiv:1502.05459 Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Integration on analytic sets and spaces, currents Simplicial Abel-Jacobi maps and reciprocity laws. With an Appendix by José Ignacio Burgos Gil
| 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 arithmetic schemes; Hasse-Weil \(L\)-functions of curves over global fields; zeta functions of elliptic curves over number fields; zeta functions of arithmetic schemes; mean-periodicity; boundary terms of zeta integrals; higher adelic analysis Ivan Fesenko, Guillaume Ricotta, and Masatoshi Suzuki, Mean-periodicity and zeta functions, Ann. Inst. Fourier (Grenoble) 62 (2012), no. 5, 1819 -- 1887 (English, with English and French summaries). Other Dirichlet series and zeta functions, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Classical almost periodic functions, mean periodic functions Mean-periodicity and zeta functions
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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 polarized regular motives; critical values of \(L\)-functions; motives over \(\mathbb{Q}\); self-dual cohomological cuspidal automorphic representations of the adeles of \(\text{GL}(n, \mathbb{Q})\); Deligne's conjecture; absolute Hodge motives; Deligne periods; Shimura varieties; period integrals; Tate conjecture on cycle classes in \(\ell\)-adic cohomology Harris, M., \textit{L}-functions and periods of polarized regular motives, J. Reine Angew. Math., 483, 75-161, (1997) Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Arithmetic aspects of modular and Shimura varieties, Representation-theoretic methods; automorphic representations over local and global fields, Variation of Hodge structures (algebro-geometric aspects), Modular and Shimura varieties \(L\)-functions and periods of polarized regular motives
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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 algebraic cycle; higher Chow group; motivic cohomology; Milnor \(K\)-theory Algebraic cycles, Higher symbols, Milnor \(K\)-theory, Formal methods and deformations in algebraic geometry, Approximation in non-Archimedean valuations Motivic cohomology of fat points in Milnor range
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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 product of elliptic curves; Milnor K-group; Albanese kernel; Jacobian variety Somekawa, M., On Milnor \textit{K}-groups attached to semi-abelian varieties, K-Theory, 4, 2, 105-119, (1990), MR 1081654 (91k:11052) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Higher symbols, Milnor \(K\)-theory, Algebraic theory of abelian varieties, Relations of \(K\)-theory with cohomology theories On Milnor K-groups attached to semi-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 representation of integers as sums of two cubes of rational numbers; Jacobian; Sylvester's conjecture; rational points on certain elliptic curves; algebraic points; action of certain Frobenius elements Rational points, Arithmetic ground fields for curves, Cubic and quartic Diophantine equations, Jacobians, Prym varieties, Waring's problem and variants Some results on the integers which are a sum of two cubes of rational numbers
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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 singularities of the theta divisor; polarized product of elliptic curves; principally polarized abelian variety R. Smith and R. Varley, ''Multiplicity \(g\) points on theta divisors,'' Duke Math. J., vol. 82, iss. 2, pp. 319-326, 1996. Theta functions and abelian varieties Multiplicity \(g\) points on theta divisors
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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 p-adic K-groups of a smooth variety; elliptic curves; higher p-adic regulator maps; values of a p-adic L-function; generalized conjecture of Birch and Swinnerton-Dyer Soulé, p-Adic K-theory of elliptic curves, Duke Math. J. 54 pp 249-- (1987) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Global ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, Elliptic curves, Special algebraic curves and curves of low genus p-adic K-theory of 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 algebraic cycles; polylogarithms; derived category of mixed motivic sheaves; motivic cohomology; higher Chow groups; effective geometric motives; Nisnevich sheaves; Tannakian category; mixed Tate motives S. Bloch, Lectures of mixed motives, in: Algebraic Geometry --- Santa Cruz 1995, Proceedings of the Symposium on Pure Mathematics, vol. 62, Part 1, American Mathematical Society, 1997, pp. 329 -- 359. Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Generalizations (algebraic spaces, stacks), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Algebraic cycles, (Co)homology theory in algebraic geometry Lectures on mixed motives
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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 moduli spaces of curves; Deligne-Mumford compactification; Chow rings; tautological rings; Faber's conjecture Carel Faber, ``Modular forms and the cohomology of moduli spaces'', Families, moduli of curves (algebraic), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), (Equivariant) Chow groups and rings; motives, Fine and coarse moduli spaces, Vector bundles on curves and their moduli Tautological algebras of moduli spaces of 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 Deligne cohomology; higher cycle (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Nonvanishing of external products for higher Chow groups
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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 two-dimensional topological quantum field theory; symplectic manifolds; moduli spaces of algebraic curves; quantum cohomology Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995), 259-367. Moduli problems for differential geometric structures, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Families, moduli of curves (analytic), Manifolds of mappings, Enumerative problems (combinatorial problems) in algebraic geometry, Calabi-Yau manifolds (algebro-geometric aspects), Topological field theories in quantum mechanics, Topological properties in algebraic geometry, Families, moduli of curves (algebraic), Topological quantum field theories (aspects of differential topology) A mathematical theory of quantum cohomology
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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 curves; algebraic curves; group schemes; modular functions; \(L\)-functions; theta functions; Fermat's last theorem; conjecture of Birch and Swinnerton-Dyer; Shimura-Taniyama-Weil conjecture; Calabi-Yau varieties; string theory; cryptography; Hopf algebroids; elliptic cohomology Husemöller, D.: Elliptic Curves. Graduate Texts in Mathematics, 2nd edn. Springer, Berlin (2004) Elliptic curves over global fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Elliptic curves, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Rational points, Special algebraic curves and curves of low genus, Global ground fields in algebraic geometry, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Research exposition (monographs, survey articles) pertaining to number theory, Calabi-Yau manifolds (algebro-geometric aspects), Elliptic genera, Research exposition (monographs, survey articles) pertaining to algebraic geometry Elliptic curves. With appendices by Otto Forster, Ruth Lawrence, and Stefan Theisen
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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 modular elliptic curve; Chow group of zero-cycles; cycle map DOI: 10.1215/S0012-7094-96-08514-2 Parametrization (Chow and Hilbert schemes), Elliptic curves, (Equivariant) Chow groups and rings; motives, Arithmetic ground fields for curves, Modular and Shimura varieties, Elliptic curves over global fields Torsion zero-cycles on the self-product of a modular 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 sigma form of Painlevé VI; two-point correlation functions of the lattice Ising model; Fuchsian linear differential equations; complete elliptic integrals; elliptic representation of Painlevé VI; scaling limit of the Ising model; susceptibility of the Ising model; singular behaviour; Fuchsian linear differential equations; apparent singularities; Landau singularities; pinch singularities; modular forms; Landen transformation; isogenies of elliptic curves; complex multiplication; Heegner numbers; moduli space of curves; pointed curves S. Boukraa, S. Hassani, J.-M. Maillard, B. M. McCoy, W. P. Orrick, and N. Zenine, ``Holonomy of the Ising model form factors,'' Journal of Physics A, vol. 40, no. 1, pp. 75-111, 2007. Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, General theory of ordinary differential operators, Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), Ordinary differential operators, Functional-differential equations (including equations with delayed, advanced or state-dependent argument), Elliptic curves, Continuum limits in quantum field theory, Other functions defined by series and integrals, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics From holonomy of the Ising model form factors to \(n\)-fold integrals and the theory of 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 \(K\)-theory; algebraic motives; Weil cohomology; Grothendieck motives; higher Chow groups; mixed motives; triangulated category; standard conjectures on algebraic cycle classes Hanamura, Math. Res. Lett. 2 pp 811-- (1995) Algebraic cycles, Generalizations (algebraic spaces, stacks), (Equivariant) Chow groups and rings; motives, Transcendental methods, Hodge theory (algebro-geometric aspects) Mixed motives and algebraic cycles. I
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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 étale cohomology; Chow groups; cokernel; kernel of the cycle class map; Pfister form; Witt ring; Albert form; unramified Witt class; function field of a quadric Bruno Kahn, Lower \Bbb H-cohomology of higher-dimensional quadrics, Arch. Math. (Basel) 65 (1995), no. 3, 244 -- 250. Algebraic theory of quadratic forms; Witt groups and rings, Galois cohomology, Étale and other Grothendieck topologies and (co)homologies, Real algebraic and real-analytic geometry, Witt groups of rings, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Lower \({\mathcal H}\)-cohomology of higher-dimensional quadrics
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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 Kummer surface; product of elliptic curves; Jacobians of stable reducible curves \(K3\) surfaces and Enriques surfaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) Equations defining reducible Kummer surfaces in \(\mathbb{P}^ 5\)
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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 cohomology; moduli spaces; curves of genus three; point counts; Galois representations; Hodge structures Bergström, Cohomology of moduli spaces of curves of genus three via point counts, J. Reine Angew. Math. Families, moduli of curves (algebraic), Transcendental methods, Hodge theory (algebro-geometric aspects) Cohomology of moduli spaces of curves of genus three via point counts
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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; Hodge theory; algebraic cycle; regulator; Deligne cohomology; Beilinson-Hodge conjecture; Abel-Jacobi map; Bloch-Beilinson filtration Algebraic cycles, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Transcendental methods, Hodge theory (algebro-geometric aspects) The business of Hodge theory and algebraic cycles
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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 linkage; vanishing theorem for the cohomology of arithmetically Buchsbaum curves; set theoretic intersection of three hypersurfaces Ellia Ph., Fiorentini M., Quelques remarques sur les courbes arithmétiquement Buchsbaum de l'espace projectif, Ann. Univ. Ferrara Sez. VII, 1987, 33, 89--111 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Special algebraic curves and curves of low genus, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) Quelques remarques sur les courbes arithmétiquement Buchsbaum de l'espace projectif. (Some remarks on the arithmetically Buchsbaum curves of the projective space)
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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 algebraic \(K\)-theory; complex surfaces; higher Chow groups; Deligne-Beilinson cohomology Pedrini, C; Weibel, C, The higher \(K\)-theory of a complex surface, Compos. Math., 129, 239-271, (2001) \(K\)-theory of schemes, Relations of \(K\)-theory with cohomology theories, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies The higher \(K\)-theory of a complex surface
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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 cohomology of finite groups; arithmetic of elliptic curves Étale and other Grothendieck topologies and (co)homologies, Elliptic curves, Cohomology of groups Cohomologies 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 direct product of elliptic curves; Hodge conjecture; abelian variety Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic theory of abelian varieties Rational cycles on abelian varieties. III
| 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 Chow group; Hodge theory; algebraic cycle; regulator; Deligne cohomology; Beilinson-Hodge conjecture; Abel-Jacobi map; Bloch-Beilinson filtration Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Transcendental methods, Hodge theory (algebro-geometric aspects) Lectures on Hodge theory and algebraic cycles
| 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; Deligne cohomology Chen X. and Lewis J.\ D., The Hodge-\({\mathcal{D}}\)-conjecture for \(K3\) and Abelian surfaces, J. Algebraic Geom. 14 (2005), no. 2, 213-240. Transcendental methods, Hodge theory (algebro-geometric aspects), \(K3\) surfaces and Enriques surfaces, (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) The Hodge-\({\mathcal D}\)-conjecture for \(K3\) and abelian surfaces
| 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 monads; higher Chow complex; operads; unital \(k\)-algebras; little \(n\)-cubes operad; tensor category; braid algebras; mixed Tate motives; symmetric monoidal category; operad of spaces; iterated loop spaces; higher Chow groups; Adams operations; derived category; integral mixed Tate modules; derived categories of modules; DGA; triangulated category; Tannakian category; Hopf algebra; co-Lie algebra; Beilinson-Soulé conjecture; operadic tensor product; cellular approximation theorem Kriz, I.; May, J. P., Operads, algebras, modules and motives, Astérisque, 233, (1995), iv+145 pp Research exposition (monographs, survey articles) pertaining to category theory, Applied homological algebra and category theory in algebraic topology, Research exposition (monographs, survey articles) pertaining to \(K\)-theory, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Homological algebra in category theory, derived categories and functors, Higher algebraic \(K\)-theory, \(K\)-theory in geometry, Generalizations (algebraic spaces, stacks) Operads, algebras, modules and 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 K3 surfaces; products of two elliptic curves; Jacobian fibrations; Mordell-Weil groups Nishiyama, K.: The Jacobian fibrations on some\textit{K}3 surfaces and their Mordell-- Weil groups. \textit{Japan. J. Math. (N.S.)}22 (1996), no. 2, 293--347. \(K3\) surfaces and Enriques surfaces, Rational points, Elliptic curves The Jacobian fibrations on some \(K3\) surfaces and their Mordell-Weil 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 conjecture of C. Voisin; arithmetic mixed sheaves; arithmetic mixed Hodge structures; second Abel-Jacobi map; zero cycles; codimension two cycles; higher Chow groups M. Saito, Arithmetic mixed sheaves , Invent. Math. 144 (2001), 533--569. \CMP1 833 893 Variation of Hodge structures (algebro-geometric aspects), Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), (Equivariant) Chow groups and rings; motives Arithmetic mixed sheaves
| 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 Chow group; algebraic cycle; regulator; Beilinson-Hodge conjecture; Abel-Jacobi map; Deligne cohomology de Jeu, R., Lewis, J.D (with an appendix by M. Asakura): Beilinson's Hodge conjecture for smooth varieties. J K-Theory \textbf{11}(2), 243-282 (2013) Algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Transcendental methods, Hodge theory (algebro-geometric aspects) Beilinson's Hodge conjecture for smooth 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 genus three curves; algebraic correspondences; Calabi-Yau threefolds; Hodge structures; variation of Hodge structures; cycle maps Calabi-Yau manifolds (algebro-geometric aspects), Special algebraic curves and curves of low genus, Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects) Algebraic correspondences between genus three curves and certain Calabi-Yau 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 Hodge conjecture; higher Chow group; Deligne cohomology Asakura, M.: On \(d\log \) of elliptic surface minus singular fibers, preprint (2006). arXiv:math/0511190v4 Transcendental methods, Hodge theory (algebro-geometric aspects), (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Hodge-type conjecture 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 period map; Schottky groups parametrized by a rigid analytic space; family of Mumford curves; p-adic Siegel half space; de Rham cohomology group; infinite automorphic product; Gauss-Manin connection; Tate curve; principal theta function L. Gerritzen,Periods and Gauss-Manin connection for families of p-adic Schottky groups, Math. Ann.275 (1986), 425--453. Local ground fields in algebraic geometry, Families, moduli of curves (analytic), Period matrices, variation of Hodge structure; degenerations, de Rham cohomology and algebraic geometry Periods and Gauss-Manin connection for families of p-adic Schottky 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 elliptic curves; cryptosystems; discrete logarithm; group of rational points; elliptic curve over a finite field; practical implementations; algorithms; running times R. Harasawa, J. Shikata, J. Suzuki, H. Imai, Comparing the MOV and FR reductions in elliptic curve cryptography, in: Advances in Cryptology--Eurocrypt '99, Lecture Notes in Computer Science, Vol. 1592, Springer, Berlin, 1999, pp. 190--205. Cryptography, Applications to coding theory and cryptography of arithmetic geometry Comparing the MOV and FR reductions in elliptic curve cryptography
| 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; modular forms; \(p\)-adic cohomology; zeta function; elliptic surfaces Elliptic curves over global fields, Holomorphic modular forms of integral weight, \(p\)-adic cohomology, crystalline cohomology, Elliptic surfaces, elliptic or Calabi-Yau fibrations On Tate's conjecture for the elliptic modular surface of level \(N\) over a prime field of characteristic \(1\mod N\)
| 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 cyclic covering of a hyperelliptic curve; isogenous to the product of two Jacobians Jacobians, Prym varieties, Coverings of curves, fundamental group Prym varieties of étale covers of hyperelliptic 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 \(p\)-adic \(L\)-functions; elliptic curves; rational points; cyclotomic characters; interpolation; projective limit of the group of global units; \(p\)-adic height Perrin-Riou, Bernadette, Fonctions \(L\) \(p\)-adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier (Grenoble), 0373-0956, 43, 4, 945-995, (1993) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Zeta functions and \(L\)-functions of number fields, Galois cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) \(p\)-adic \(L\)-functions of an elliptic curve and rational points
| 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 hyperbolic fibre space; higher dimensional analogue of Mordell's conjecture for curves; hyperbolic manifolds; algebraic families of hyperbolic varieties; Mordell's conjecture over function fields Noguchi, J.Hyperbolic fiber spaces and Mordell's conjecture over function fields, Publ. Research Institute Math. Sciences Kyoto University21, No. 1 (1985), 27--46. Hyperbolic and Kobayashi hyperbolic manifolds, Holomorphic bundles and generalizations, Families, moduli, classification: algebraic theory Hyperbolic fibre spaces and Mordell's conjecture over function 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 varieties over a finite fields; zeta functions; bielliptic surfaces; albanese mapping; elliptic curves; étale cohomology; Frobenius morphism; isogeny class Рыбаков, С. Ю., Дзета-функции биэллиптических поверхностей над конечными полями, Матем. заметки, 83, 2, 273-285, (2008) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Zeta functions and \(L\)-functions, Finite ground fields in algebraic geometry Zeta functions of bielliptic surfaces 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 \(K\)-group; semi-abelian varieties; product of curves over a finite field B. Kahn, Nullité de certains groupes attachés aux variétés semi-abéliennes sur un corps fini; application, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 13, 1039--1042. Abelian varieties and schemes, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry Nullité de certains groupes attachés aux variétés semi- abéliennes sur un corps fini. Application. (Vanishing of certain groups attached to semi-abelian varieties over a finite field. Application)
| 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 integral points; Lang's conjecture; canonical height; Szpiro's conjecture; discriminant; bound for the number of torsion points on elliptic curves [10]M. Hindry and J. H. Silverman, The canonical height and integral points on elliptic curves, Invent. Math. 93 (1988), 419--450. Arithmetic ground fields for curves, Elliptic curves, Global ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Rational points The canonical height and integral points 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 elliptic curves; mappings; isogenies; orders of elliptic curves; \(j\)-invariants Elliptic curves, Complex multiplication and abelian varieties, Elliptic curves over local fields On isomorpic K-rational groups of isogenous 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 Galois representations; varieties over local ground fields; étale cohomology; motivic Galois representations; elliptic curves J. Coates, R. Sujatha and J.-P. Wintenberger, On the Euler-Poincaré characteristics of finite dimensional \(p\)-adic Galois representations, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 107-143. Galois representations, \(p\)-adic theory, local fields, Local ground fields in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Motivic cohomology; motivic homotopy theory, Elliptic curves over local fields On the Euler-Poincaré characteristics of finite dimensional \(p\)-adic Galois representations.
| 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 rings; moduli spaces of curves; Chow motives; twisted commutative algebras Families, moduli of curves (algebraic), Algebraic cycles, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Classifying spaces of groups and \(H\)-spaces in algebraic topology Tautological classes with twisted coefficients
| 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 arithmetic function; number of factorizations of an integer; group of rational points; elliptic curves Arithmetic functions; related numbers; inversion formulas, Cubic and quartic Diophantine equations, Elliptic curves Some arithmetic functions associated with diophantine equations
| 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 generalization of class field theory; local fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor; global fields Class field theory, Class field theory; \(p\)-adic formal groups, Higher symbols, Milnor \(K\)-theory, \(K\)-theory of global fields, \(K\)-theory of local fields, Ramification and extension theory, Formal groups, \(p\)-divisible groups, Generalized class field theory (\(K\)-theoretic aspects) Generalization of class field 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 Borel conjecture; \(L^ 2\)-cohomology of locally symmetric varieties; modular curves; automorphic forms; intersection cohomology; Zucker conjecture Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) A brief introduction to the \(L^ 2\)-cohomology of locally symmetric 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 Gromov-Witten invariants; enumerative geometry; number of elliptic plane curves Pandharipande, R, Counting elliptic plane curves with fixed \(j\)-invariant, Proc. Am. Math. Soc., 125, 3471-3479, (1997) Enumerative problems (combinatorial problems) in algebraic geometry, Elliptic curves Counting 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 number of non-rational subfields; number of separable subfields; number of morphisms of algebraic curves; Chow coordinates; theorem of the base; Jacobian; genus; function field; Angle theorem; de Franchis' theorem E. Kani, Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. Zbl0615.12017 MR842053 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Birational geometry, Jacobians, Prym varieties, Divisors, linear systems, invertible sheaves, Special surfaces Bounds on the number of non-rational subfields of a function field
| 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 bundle (=pencil) of plane algebraic curves; bundle (=pencil) of conics; cyclic points at infinity; bundle (=pencil) of circles; theorem of the three conics Questions of classical algebraic geometry, Projective analytic geometry, Projective techniques in algebraic geometry Projectivities between bundles of plane higher order 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 subvarieties of moduli spaces of curves; effective cones; higher codimensional cycles; hyperelliptic curves Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, Families, moduli of curves (algebraic), Special algebraic curves and curves of low genus, Algebraic cycles Hyperelliptic classes are rigid and extremal in genus two
| 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 formal characters of torus; connected, reductive algebraic group; Borel subgroup; character group; Hochschild cohomology; Weyl's character formula; Kostant's multiplicity formula; Steinberg's tensor product formula Cohomology theory for linear algebraic groups, Representation theory for linear algebraic groups, Classical groups (algebro-geometric aspects) A new proof of old character formulas
| 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 degeneration; flat families of subschemes; codimension two; subcanonical space curves; complete intersection space curve Low codimension problems in algebraic geometry, Complete intersections, Projective and enumerative algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Formal methods and deformations in algebraic geometry Some problems on the degeneration of projective 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 generators of modules; Chow group; zero-cycle Commutative rings and modules of finite generation or presentation; number of generators, Algebraic cycles Generation of modules and transcendence degree of zero-cycles
| 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 conjecture of Beilinson and Bloch; rank of the Griffiths group; smooth projective variety over a number field; order of vanishing of an L-function; elliptic curves J. Buhler, C. Schoen, and J. Top, ''Cycles, \(L\)-functions and triple products of elliptic curves,'' J. reine angew. Math., vol. 492, pp. 93-133, 1997. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Varieties over global fields, Algebraic cycles, Global ground fields in algebraic geometry Cycles, \(L\)-functions and triple products 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 Abel-Jacobi map; cycle class; higher Chow cycle (Equivariant) Chow groups and rings; motives, Algebraic cycles A remark on the second Abel-Jacobi map
| 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-step flag manifolds; puzzle conjecture; cohomology product structure constants; small quantum cohomology A. Buch, A. Kresch, K. Purbhoo, and H. Tamvakis. ''The puzzle conjecture for the cohomol ogy of two-step flag manifolds''. 2014. arXiv:1401.1725. Symmetric functions and generalizations, Classical problems, Schubert calculus, Grassmannians, Schubert varieties, flag manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) The puzzle conjecture for the cohomology of two-step flag manifolds
| 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 Brauer groups of elliptic curves; torsion; group of rational points; non-dyadic elliptic curve Elliptic curves, Brauer groups of schemes The Brauer groups and the torsion of local 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 regulator map; Deligne cohomology; holomorphic gerbes; sheaves of categories Brylinski, J.-L., Holomorphic gerbes and the Beilinson regulator, Strasbourg, 1992. Strasbourg, 1992, Astérisque, 226, 8, 145-174, (1994), \textit{K}-theory Relations of \(K\)-theory with cohomology theories, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Nonabelian homological algebra (category-theoretic aspects) Holomorphic gerbes and the Beilinson regulator
| 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 stable curves; Deligne-Mumford semistable curves; Simpson scheme López~Martín, A.C., Simpson Jacobians of reducible curves, J. reine angew. math., 582, 1-39, (2005) Families, moduli of curves (algebraic), Jacobians, Prym varieties, Vector bundles on curves and their moduli, Picard groups, Schemes and morphisms, Families, moduli of curves (analytic) Simpson Jacobians of reducible 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 motivic cohomology complexes; polylogarithm; higher Chow groups; motives Lichtenbaum, S.: Motivic complexes. In: Motives (Seattle, WA, 1991), pp. 303--313 Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(p\)-adic cohomology, crystalline cohomology, Generalizations (algebraic spaces, stacks), Algebraic cycles, Relations of \(K\)-theory with cohomology theories Motivic complexes
| 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 Tate constant; hypergeometric differential equation; Legendre family of elliptic curves; Tate curve; Picard-Fuchs equation; Hasse-Witt matrix; formal group Local ground fields in algebraic geometry, Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) On the Tate-matrix
| 0 |
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