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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 quadratic form; function field of a quadratic form; \(u\)-invariant; quadratic forms with maximal splitting; torsion of Chow groups of quadrics; unramified cohomology of quadrics Izhboldin, O. T., Fields of \(u\)-invariant 9, Ann. of Math., 154, 529-587, (2001) Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Galois cohomology, (Equivariant) Chow groups and rings; motives, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Fields of \(u\)-invariant \(9\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus \(g\); Green's conjecture; Koszul cohomology Special algebraic curves and curves of low genus Some matrices related to Green's conjecture
| 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 Hamiltonian families of curves on three-dimensional manifolds Families, moduli of curves (analytic), Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Hamiltonian families of rational 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 Jacobian varieties; curves of genus three J. Romero-Valencia and A.G. Zamora, Explicit constructions for genus 3 Jacobians, Preprint (2009), arXiv:math/0904.4537v1[math.AG]. Jacobians, Prym varieties, Plane and space curves Explicit constructions for genus 3 Jacobians
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Elliptic curve cryptography; oblivious transfer; one-out-of-two oblivious transfer DOI: 10.1080/01611190601144478 Cryptography, Applications to coding theory and cryptography of arithmetic geometry Oblivious transfer using 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 cohomology of moduli spaces of curves; curves over finite fields; hyperelliptic curves J. Bergström, Equivariant counts of points of the moduli spaces of pointed hyperelliptic curves, Doc. Math. 14 (2009), 259-296. Families, moduli of curves (algebraic), Curves over finite and local fields, Transcendental methods, Hodge theory (algebro-geometric aspects) Equivariant counts of points of the moduli spaces of pointed 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 intersection theory of moduli spaces of curves; matroid Chow rings; polynomials of matroids Combinatorial aspects of matroids and geometric lattices, Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Matroid psi classes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Picard numbers; rank of the Mordell-Weil group; elliptic curves over function fields; automorphisms Peter F. Stiller, The Picard numbers of elliptic surfaces with many symmetries, Pacific J. Math. 128 (1987), no. 1, 157 -- 189. Picard groups, Special surfaces, Group actions on varieties or schemes (quotients) The Picard numbers of elliptic surfaces with many symmetries
| 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 cohomology; integration along the fibers; cohomology product Dupont, JL; Ljungmann, R, Integration of simplicial forms and Deligne cohomology, Math. Scand., 97, 11-39, (2005) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Other homology theories in algebraic topology, Differential forms in global analysis Integration of simplicial forms 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 surfaces of general type; \(p_g=0\); homology groups; products of curves; actions of finite abelian group; isotrivial fibrations; surfaces isogenous to a product; fake quadrics; branched coverings; fundamental group Surfaces of general type, Classical real and complex (co)homology in algebraic geometry, Series and lattices of subgroups Homology of some surfaces with \( p_g = q = 0\) isogenous to a product
| 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 Albanese variety; algebraic cycles; second cohomology group of a surface with prescribed singularities; curves on surfaces; effective divisor; 1- motive; periods (Co)homology theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Algebraic cycles, Singularities of surfaces or higher-dimensional varieties, Curves in algebraic geometry On glueing curves on surfaces and 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 efficient elliptic curve arithmetic; point multiplication; Jacobi model of elliptic curves Hisil, H., Wong, K.K.-H., Carter, G., Dawson, E.: Jacobi quartic curves revisited. In: Boyd, C., González Nieto, J. (eds.) ACISP 2009. LNCS, vol. 5594, pp. 452--468. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-02620-1_31 Cryptography, Applications to coding theory and cryptography of arithmetic geometry Jacobi quartic curves revisited
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; A-infinity-algebra; Hochschild cohomology; deformation theory Polishchuk, A.: Moduli of curves as moduli of \(A_\infty \)-structures. Duke Math. J. (to appear). arXiv:1312.4636 Families, moduli of curves (algebraic), Differential graded algebras and applications (associative algebraic aspects) Moduli of curves as moduli of \(A_\infty\)-structures
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves asymptotic theory of codes; algebraic curves; modular curves; elliptic modules Manin, Y. I.; A\check{}, S. G. Vl: Linear codes and modular curves. J. soviet math. 30, 2611-2643 (1985) Linear codes (general theory), Arithmetic ground fields for curves, Applications to coding theory and cryptography of arithmetic geometry Linear codes and modular 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 evaluation of L-series; Birch Swinnerton-Dyer conjecture; elliptic curve; Galois cohomology G. Frey: A relation between the value of the L-series of the curve:y 2=x 3-k 3 ins=1 and its Selmer group, Arch. Math. 45, 232--238 (1985) Special algebraic curves and curves of low genus, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Galois cohomology, Elliptic curves, Holomorphic modular forms of integral weight A relation between the value of the L-series of the curve: \(y^ 2=x^ 3-k^ 3\) in \(s=1\) and its Selmer group
| 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 groups of elliptic curves with integral j-invariant; pure cubic number fields Fung, G.; Ströher, H.; Williams, H.; Zimmer, H.: Torsion groups of elliptic curves with integral j-invariant over pure cubic fields. J. number theory 36, 12-45 (1990) Elliptic curves, Computational aspects of algebraic curves, Cubic and quartic extensions, Global ground fields in algebraic geometry Torsion groups of elliptic curves with integral j-invariant over pure cubic 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 computational problems; supersingular elliptic curves; isogeny graphs; endomorphism rings; constructive versions of Deuring's correspondence Cryptography, Computational aspects of algebraic curves Supersingular isogeny graphs and endomorphism rings: reductions and solutions
| 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 rationality; moduli spaces of marked curves; twisted forms; Galois cohomology; Brauer group Rational and unirational varieties, Rationality questions in algebraic geometry, Families, moduli of curves (algebraic), Linear algebraic groups over arbitrary fields, Brauer groups (algebraic aspects) The rationality problem for forms of \(\overline{M}_{0,n}\)
| 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 elliptic curves; rational points of order 2 --------, On the rank of elliptic curves with three rational points of order \(2\) , Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 77-78. Elliptic curves over global fields, Elliptic curves, Rational points On the rank of elliptic curves with three rational points of order 2
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves schemes; coherent sheaves; cohomology of schemes; duality theory; algebraic curves; birational geometry of surfaces; arithmetic algebraic curves; arithmetic algebraic surfaces; stable reduction of curves; arithmetic algebraic geometry; birational geometry of algebraic surfaces Q. Liu, \(Algebraic Geometry and Arithmetic Curves\) (Oxford University Press, Oxford, 2006) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Schemes and morphisms, Arithmetic varieties and schemes; Arakelov theory; heights, Birational geometry Algebraic geometry and arithmetic curves. Transl. by Reinie Erné
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of Riemann surfaces; Calabi-Yau elliptic space; Frobenius algebra; heat kernel; ultra-violet divergence; topological conformal field theory; modular operad; orbi-cell complex; open topological field theory; Deligne-Mumford compactification Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Fine and coarse moduli spaces, Algebraic topology of manifolds, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry On the extension of a TCFT to the boundary of the moduli space
| 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 rational points; elliptic curves; modular forms; area of right triangle with rational sides; survey; congruent numbers; students education Fibonacci and Lucas numbers and polynomials and generalizations, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Elliptic curves, Linear Diophantine equations, Holomorphic modular forms of integral weight Congruent numbers - from elementary to algebraic number 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 Bibliography; \(L_ 2\)-cohomology; \(\mathbb{D}\)-modules; Beilinson cohomology; regulator maps; Grothendieck motives; degeneration of Hodge structures; intersection homology; Riemann-Hilbert correspondence; Deligne cohomology; variation of mixed Hodge structure; Higgs bundles Brylinski, J.-L., Zucker, S.: An overview of recent advances in Hodge theory. In: Several Complex Variables VI. Encyclopedia Math. Sci., vol. 69, pp. 39--142. Springer, Berlin (1990) Transcendental methods, Hodge theory (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Variation of Hodge structures (algebro-geometric aspects), Mixed Hodge theory of singular varieties (complex-analytic aspects), History of algebraic geometry, Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), History of mathematics in the 20th century An overview of recent advances in Hodge 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 families of rational curves; smooth compactification; Grassmann variety; Quot scheme; Chow ring Strømme, S A, On parametrized rational curves in Grassmann varieties., Lecture Notes in Math, 1266, 251-272, (1987) Grassmannians, Schubert varieties, flag manifolds, Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes), Homogeneous spaces and generalizations, Algebraic moduli problems, moduli of vector bundles On parametrized rational curves in Grassmann 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 Sato-Tate conjecture; parametric families of elliptic curves Elliptic curves over global fields, Curves over finite and local fields, Elliptic curves The Sato-Tate distribution in thin parametric families 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 points on complete intersection of two curves; Cayley-Bacharach theorem Special algebraic curves and curves of low genus, Complete intersections A generalization of the Cayley-Bacharach theorem
| 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; isogenies; additive reduction; parameterized families of elliptic curves Elliptic curves over global fields, Isogeny, Families, moduli of curves (algebraic), Elliptic curves Explicit classification of isogeny graphs of rational 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 limit linear series; higher Picard group; higher Jacobian; complex curve; isomorphism classes of line bundles of degree \(d\); Albanese variety; moduli space of pointed curves Ciro Ciliberto, Joe Harris, and Montserrat Teixidor i Bigas, On the endomorphisms of \?\?\?(\?\textonesuperior _{\?}(\?)) when \?=1 and \? has general moduli, Classification of irregular varieties (Trento, 1990) Lecture Notes in Math., vol. 1515, Springer, Berlin, 1992, pp. 41 -- 67. Jacobians, Prym varieties, Families, moduli of curves (algebraic), Picard schemes, higher Jacobians, Divisors, linear systems, invertible sheaves On the endomorphisms of \(\text{Jac}(W_ d^ 1(C))\) when \(\rho=1\) and \(C\) has general moduli
| 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 homotheties in the image of Galois representations; elliptic curves; torsion points; isogeny; Borel subgroup A. David, Caractère d'isogénie et borne uniforme pour les homothéties, PhD thesis, IRMA, Strasbourg, 2008. Galois representations, Elliptic curves over global fields, Global ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties Isogenic character and uniform bound for homotheties
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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 incidences; curves in three dimensions; degrees of freedom; polynomial partition; anchored circles; directed points Erdős problems and related topics of discrete geometry, Transversal (matching) theory, Plane and space curves Incidences between points and curves with almost two degrees of freedom
| 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 2; isomorphism classes of elliptic curves over finite ground field; Weierstrass form; number of points Menezes A., Vanstone S.: Isomorphism classes of elliptic curves over finite fields of characteristic 2. Utilitas Math. \textbf{38}, 135-154 (1990). Elliptic curves, Finite ground fields in algebraic geometry Isomorphism classes of elliptic curves over finite fields of characteristic 2
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves finite field; family of varieties; monodromy; quadratic excess; genus-\(g\)-curves; degree-\(d\) hypersurfaces; geometric monodromy group; Frobenius-Schur indicator; family of higher-dimensional varieties; Deligne equidistribution theorem Katz, N.: Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Finite Fields Appl. \textbf{7}(1), 45-69 (2001). (Dedicated to Professor Chao Ko on the occasion of his 90th birthday) Curves over finite and local fields, Arithmetic ground fields (finite, local, global) and families or fibrations, Structure of families (Picard-Lefschetz, monodromy, etc.) Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess
| 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-Beilinson homology and cohomology; Poincaré duality; mixed motives; analogue of mixed Hodge structures Uwe Jannsen, Deligne homology, Hodge-\?-conjecture, and motives, Beĭlinson's conjectures on special values of \?-functions, Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 305 -- 372. (Co)homology theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Sheaves of differential operators and their modules, \(D\)-modules Deligne homology, Hodge-\({\mathcal D}\)-conjecture, 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 earlier history of elliptic curves; Diophantus; Fermat; Newton; elliptic integrals; elliptic functions Elliptic curves over global fields, Elliptic curves, History of number theory, History of algebraic geometry Elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher Hasse-Witt matrices; formal group laws; length of a jump; sequence for abelian varieties; unit root crystal; hyperelliptic; curves Ditters, E.J.: On the classification of commutative formal group laws overp-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices. Math. Z.202, 83--109 (1989) Formal groups, \(p\)-divisible groups, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special algebraic curves and curves of low genus On the classification of commutative formal group laws over p-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves proof of Mordell conjecture; proof of Tate conjecture; proof of; Shafarevich conjecture; height of Abelian variety; rational points; on elliptic curves Deligne, P., Preuve des conjectures de Tate et de shafarevitch (d'après G. faltings), Asterisque, 121-122, 25-41, (1985) Arithmetic ground fields for abelian varieties, Rational points, Global ground fields in algebraic geometry, Elliptic curves, Special algebraic curves and curves of low genus Preuve des conjectures de Tate et de Shafarevitch [D'après G. Faltings]. (Proof of the conjecture of Tate and Shafarevich [After G. Faltings])
| 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 Brill-Noether curve; limit linear series; genus; chains of elliptic curves Castorena, A.; López Martín, A.; Teixidor i Bigas, M., Invariants of the brill-Noether curve, Adv. geom., 17, 1, 39-52, (2017) Vector bundles on curves and their moduli, Special divisors on curves (gonality, Brill-Noether theory) Invariants of the Brill-Noether 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 equations over finite fields; elliptic curves; diophantine equations in two variables; quadratic residues; large sieve; Mordell's theorem; Riemann Roch theorem; rational points; integral points; Thue equation; superelliptic equations; nonstandard arithmetic; Hilbert's tenth problem Stepanov, SA: Arithmetic of Algebraic Curves Translated from the Russian by Irene Aleksanova. Monographs in Contemporary Mathematics. Consultants Bureau, New York (1994). Elliptic curves over global fields, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Elliptic curves, Elliptic curves over local fields, Multiplicative and norm form equations Arithmetic of algebraic curves. Transl. from Russian by Irene Aleksanova
| 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 algebraic \(K\)-theory; values of \(L\)-functions; Beilinson conjecture; finite dimensional representations of graded pro-Lie algebra; polylogarithms; Bernoulli numbers; Riemann zeta-function; generic functional equation; trilogarithm; Bloch-Wigner function; Spence-Kummer relation; motivic cohomology; characteristic classes; Dedekind zeta function; number field; dilogarithm; regulator map; Deligne-Beilinson cohomology; mixed Tate category; Tannakian categories; duality of configurations; Grassmannian trilogarithm M. Prausa, \textit{epsilon: A tool to find a canonical basis of master integrals}, arXiv:1701.00725 [INSPIRE]. Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Zeta functions and \(L\)-functions of number fields, \(K\)-theory of global fields, Other functions defined by series and integrals Geometry of configurations, polylogarithms, and motivic cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; characteristic two; multiplication; Frobenius expansion; Frobenius endomorphism Müller, V.: Fast multiplication on elliptic curves over small fields of characteristic two. J. cryptol. 11, 219-234 (1998) Number-theoretic algorithms; complexity, Computational aspects of algebraic curves, Cryptography, Elliptic curves, Elliptic curves over global fields Fast multiplication on elliptic curves over small fields of characteristic 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 \(p\)-adic Hodge theory; characteristic \(p\); crystalline cohomology; Hodge numbers; tensor product of weakly admissible filtered isocrystals; geometric invariant theory Totaro, B., Tensor products in \textit{p}-adic Hodge theory, Duke Mathematical Journal, 83, 1, 79-104, (1996) \(p\)-adic cohomology, crystalline cohomology, Transcendental methods, Hodge theory (algebro-geometric aspects), Local ground fields in algebraic geometry Tensor products in \(p\)-adic Hodge 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 algebraic \(K\)-theory; Bloch-Quillen formula; Gersten spectral sequence; sheaves of higher \(K\)-groups; torsion; higher Chow groups; relative Chow group; Picard groups S. E. Landsburg, ''Relative Chow groups,'' Illinois J. Math., vol. 35, iss. 4, pp. 618-641, 1991. \(K\)-theory of schemes, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles Relative 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 Arakelov theory; singular surfaces; algebraic curves; moduli spaces; moduli stacks; enumerative geometry of moduli spaces; Deligne pairing L. Weng, \(\Omega\) -admissible theory, II: Deligne pairings over moduli spaces of punctured Riemann surfaces, Math. Ann. 320 (2001), 239--283. Arithmetic varieties and schemes; Arakelov theory; heights, Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Generalizations (algebraic spaces, stacks) \(\Omega\)-admissible theory. II: Deligne pairings over moduli spaces of punctured Riemann surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves number of rational points; Deligne-Lusztig curves; function fields; large groups of automorphisms; Goppa codes HP Johan~P. Hansen and Jens~Peter Pedersen, \emph Automorphism groups of Ree type, Deligne-Lusztig curves and function fields, J. Reine Angew. Math. \textbf 440 (1993), 99--109. Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic ground fields for curves, Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Automorphism groups of Ree type, Deligne-Lusztig curves and 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 generalized Kummer varieties; Chow group of zero-cycles; Bloch-Beilinson filtration; Beauville conjecture; constant cycle subvarieties (Equivariant) Chow groups and rings; motives, Algebraic cycles Corrigendum to: ``On the Chow group of zero-cycles of a generalized Kummer variety''
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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 minimal compactification of a symmetric homogeneous space; intersection product; wonderful compactifications; Chow ring; torus embeddings De Concini, C.; Procesi, C., \textit{complete symmetric varieties II: intersection theory}, Algebraic groups and related topics (Kyoto/Nagoya, 1983), 481-513, (1985), North-Holland Enumerative problems (combinatorial problems) in algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Homogeneous spaces and generalizations Complete symmetric varieties. II: Intersection theory
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Quantum Schubert Calculus of homogeneous spaces; Pontryagin product, loop groups, Equivariant homology and cohomology of homogeneous spaces, Gromov-Witten invariants Leung, N. C.; Li, C., Gromov-Witten invariants for \(G / B\) and Pontryagin product for {\(\omega\)}\textit{K}, Trans. Amer. Math. Soc., 5, 2567-2599, (2012) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Grassmannians, Schubert varieties, flag manifolds, Infinite-dimensional Lie groups and their Lie algebras: general properties Gromov-Witten invariants for \(G/B\) and Pontryagin product for \(\Omega K\)
| 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 surfaces isogenous to a product of curves; surfaces of general type; groups of small order; MAGMA's library Bauer, I.; Catanese, F.; Grunewald, F., The classification of surfaces with \(p_g = q = 0\) isogenous to a product of curves, Special Issue: In Honor of Fedor Bogomolov. Part 1. Special Issue: In Honor of Fedor Bogomolov. Part 1, Pure Appl. Math. Q., 4, 2, 547-586, (2008) Moduli, classification: analytic theory; relations with modular forms, Surfaces of general type The classification of surfaces with \(p_g=q=0\) isogenous to a product 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 geometric invariant theory; blowing up; partial desingularisation; rational cohomology; moduli spaces of hyperelliptic curves F. C. Kirwan, ''Partial desingularisations of quotients of nonsingular varieties and their Betti numbers,'' Ann. of Math., vol. 122, iss. 1, pp. 41-85, 1985. Global theory and resolution of singularities (algebro-geometric aspects), Group actions on varieties or schemes (quotients), Geometric invariant theory, Algebraic moduli problems, moduli of vector bundles, Classical real and complex (co)homology in algebraic geometry Partial desingularisations of quotients of nonsingular varieties and their Betti 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 two dimensional global fields; algebraic function field in one; variable over algebraic number field; Galois cohomology group; \(H^ 3\); Hasse principles; local-global principles; reduced norms; division algebras; quadratic forms; sum of squares K.~Kato, {A {H}asse principle for two dimensional global fields. With an appendix by {J}.-{L} {C}olliot-{T}hélène.}, J. Reine Angew. Math. {366} (1986), 142--180. DOI 10.1515/crll.1986.366.142; zbl 0576.12012; MR0833016 Galois cohomology, Brauer groups of schemes, Quadratic forms over global rings and fields, Galois cohomology, Quaternion and other division algebras: arithmetic, zeta functions, Waring's problem and variants, Arithmetic theory of algebraic function fields A Hasse principle for two dimensional global fields. Appendix by Jean-Louis Colliot-Thélène
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus 1; elliptic curves; integer points; height; Weierstrass curves [12] W. M. Schmidt, \(Integer points on curve on genus \)1
\[
, Compositio Math. 81 (1992), 33-59. Numdam | &MR 11 | &Zbl 0747.
\]
Elliptic curves over global fields, Cubic and quartic Diophantine equations, Elliptic curves, Arithmetic ground fields for curves Integer points on curves of genus 1
| 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 Eisenstein symbol map; motivic cohomology; Néron model; Bernoulli polynomials; boundary maps; K-theory; place of bad reduction; elliptic curve; modular curve Schappacher, N.; Scholl, A. J., \textit{the boundary of the Eisenstein symbol}, Math. Ann., 290, 303-321, (1991) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Symbols and arithmetic (\(K\)-theoretic aspects), Higher symbols, Milnor \(K\)-theory The boundary of the Eisenstein symbol
| 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 arithmetical theory of modular functions; complex multiplication of elliptic functions; FdM 18, 396; modular curves; automorphic representations; \(\ell \)-adic representations; Drinfeld theory; elliptic modules; error-correcting codes; elliptic curves Research exposition (monographs, survey articles) pertaining to number theory, Modular and automorphic functions, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Modular and Shimura varieties, Families, moduli of curves (algebraic), History of mathematics in the 19th century, Collected or selected works; reprintings or translations of classics, History of number theory Kronecker's Jugendtraum and modular functions. Transl. from the Russian by M. Tsfasman
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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 \(SU(2)\) WZNW model; family of elliptic curves Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), Elliptic curves, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics A system of differential equations associated with conformal field theory on 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 transcendental algebraic geometry; Kählerian geometry; Hodge theory; Hodge decomposition; Lefschetz decomposition; Hodge index theorem; de Rham complex; Frölicher spectral sequence; variations of Hodge structures; period domain; algebraic cycles; Deligne cohomology; Abel-Jacobi map C. Voisin, \textit{Hodge theory and complex algebraic geometry. I}. Translated from the French original by Leila Schneps, Cambridge Studies in Advanced Mathematics, 76, Cambridge University Press, Cambridge, 2002.Zbl 1005.14002 MR 1967689 Transcendental methods, Hodge theory (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Algebraic cycles, Transcendental methods of algebraic geometry (complex-analytic aspects), Variation of Hodge structures (algebro-geometric aspects), Period matrices, variation of Hodge structure; degenerations Hodge theory and complex algebraic geometry. I. Translated from the French by Leila Schneps
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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 variety; Baily-Borel compactification; cusp; Chow group; Manin-Drinfeld theorem; modular unit; higher Chow cycle (Equivariant) Chow groups and rings; motives, Modular and Shimura varieties, Other groups and their modular and automorphic forms (several variables), Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms Rational equivalence of cusps
| 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 of simple deficient elliptic curves Elliptic curves A boundedness theorem for the torsion of a class of elliptic curves over algebraic number 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 elliptic surfaces; action of automorphisms on cohomology Cai, J.-X., Automorphisms of elliptic surfaces, inducing the identity in cohomology, J. Algebra, 322, 12, 4228-4246, (2009) Elliptic surfaces, elliptic or Calabi-Yau fibrations Automorphisms of elliptic surfaces, inducing the identity in 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 vanishing of the cohomology; stable rank two vector bundle DOI: 10.1080/00927879508825345 Vanishing theorems in algebraic geometry Some vanishings for the cohomology of rank 2 stable reflexive sheaves on \(\mathbb{P}^ 3\) and for their restriction to a general plane
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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 quadratic spaces; survey; orthogonal bundles; Pfaffians; discriminants; involutions; linear algebraic groups; Witt groups; Clifford invariant; hyperelliptic curves; Chow groups; etale cohomology R. Parimala , Study of quadratic forms-some connections with geometry . Proc. of the Int. Cong. of Mathematicians , Vol. 1 , 2 ( Zürich , 1994 ), 324 - 332 , Birkhäuser , Basel , 1995 . MR 1403933 | Zbl 0851.11025 Quadratic spaces; Clifford algebras, Algebraic theory of quadratic forms; Witt groups and rings, Algebraic cycles, Étale and other Grothendieck topologies and (co)homologies Study of quadratic forms -- Some connections with 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 \(dg\)-operads; gravity algebras; polycommutative; punctured Riemann spheres; stratification of compactified moduli space; homology characters; moduli spaces; quantum cohomology; compact Kähler manifolds; Knudsen-Deligne-Mumford compactification; spectral sequence; mixed Hodge theory Getzler, E.: Operads and moduli spaces of genus \(0\) Riemann surfaces. In Dijkgraaf, R., Faber, C., van der Gerr, G. (eds.) The Moduli Space of Curves, volume 129 of \textit{Progress in Mathematics}, pp. 199-230. Birkhäuser, Basel (1995) Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Homological algebra in category theory, derived categories and functors, Applications of differential geometry to physics, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Other \(n\)-ary compositions \((n \ge 3)\), Quantization in field theory; cohomological methods Operads and moduli spaces of genus 0 Riemann surfaces
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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 \(L\)-functions of symmetric representations; characteristic \(p\) Igusa curves; number of rational points; first étale cohomology groups; Hecke polynomials Amílcar Pacheco, Rational points on Igusa curves and \?-functions of symmetric representations, J. Number Theory 58 (1996), no. 2, 343 -- 360. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Rational points, Cohomology of arithmetic groups, Elliptic curves Rational points on Igusa curves and \(L\)-functions of symmetric representations
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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 textbook (algebraic geometry); algebraic curves; projective varieties; abelian categories; schemes; cohomology of schemes; intersection theory; duality theory Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Foundations of algebraic geometry, Schemes and morphisms, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Riemann-Roch theorems, Plane and space curves, Definitions and generalizations in theory of categories A royal road to algebraic 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 representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (2003). Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory, Group schemes, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over arbitrary fields Representations of algebraic 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 cohomological Galois theory; topoi; sites; arithmetic curves; algebraic Teichmüller theory; modular groups; elliptic curves; moduli theory of curves; conformal field theories Grothendieck, Alexandre: La longue marche à travers la théorie de Galois tome 1, (1995) Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Topoi, Galois cohomology The long march through Galois theory. Vol. 1. Transcription of an unpublished manuscript. Edited and with a foreword by Jean Malgoire
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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 Hochschild homology; higher algebraic K-theory of seminormal curves; graded algebras; cyclic homology Geller, S.; Reid, L.; Weibel, C., The cyclic homology and \(K\)-theory of curves, J.~Reine Angew. Math., 393, 39-90, (1989) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Curves in algebraic geometry, Grothendieck groups, \(K\)-theory and commutative rings The cyclic homology and K-theory 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 modular varieties; cyclic isogenies of elliptic curves; Shimura varieties Modular and Shimura varieties, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic aspects of modular and Shimura varieties, Elliptic curves Singularities of the modular 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 functions of a complex variable; holomorphic functions; meromorphic functions; geometric function theory; elliptic functions; elliptic integrals; elliptic curves Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable, Analytic continuation of functions of one complex variable, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Meromorphic functions of one complex variable (general theory), Analytic theory of abelian varieties; abelian integrals and differentials Foundations of function theory. An introduction to complex analysis and its applications. For Bachelor and diploma degrees
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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 singular curves; zero-dimensional schemes; vanishing of cohomology; Horace method Singularities of curves, local rings, Vanishing theorems in algebraic geometry, Singularities in algebraic geometry Imposing singular points and many nodes to curves on surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves ordinary points of curves; higher derivation; common uniformizing parameter Brown, W.C.: A note on higher derivatives and ordinary points of curves. Rocky Mt. J. Math.14, 397--402 (1984) Morphisms of commutative rings, Local rings and semilocal rings, Singularities of curves, local rings, Ramification problems in algebraic geometry A note on higher derivations and ordinary points 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 Bibliography; torsion points; L-series; Heegner points; arithmetic of elliptic curves; elliptic curves; elliptic curves over number fields; bibliography Frey, G.: Some aspects of the theory of elliptic curves over number fields. Exposition. math. 4, 35-66 (1986) Special algebraic curves and curves of low genus, Elliptic curves, Arithmetic ground fields for curves Some aspects of the theory of elliptic curves over number 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 Jacobian of modular curve; number of isogeny classes of elliptic curves; quotients of the Jacobian Jacobians, Prym varieties, Isogeny, Elliptic curves, Elliptic curves over local fields, Local ground fields in algebraic geometry On modular 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 nilpotent groups; zeta functions; elliptic curves; rational points; numbers of subgroups; subgroups of finite index Nilpotent groups, Other Dirichlet series and zeta functions, Elliptic curves, Associated Lie structures for groups, Rational points, Subgroup theorems; subgroup growth Associating curves of low genus to infinite nilpotent groups via the zeta function.
| 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 Milnor \(K\)-groups; Chow groups; products of curves; \(p\)-adic field Raskind, Wayne; Spiess, Michael, Milnor \textit{K}-groups and zero-cycles on products of curves over \textit{p}-adic fields, Compos. Math., 121, 1, 1-33, (2000), MR 1753108 (2002b:14007) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Local ground fields in algebraic geometry, (Equivariant) Chow groups and rings; motives, Polylogarithms and relations with \(K\)-theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Milnor \(K\)-groups and zero-cycles on products of curves over \(p\)-adic 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 elliptic curves; special values of \(L\)-functions \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Elliptic curves Central values of \(L\)-functions of cubic twists
| 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 real trigonal curves; real algebraic curves of type I; inflexion point; dessins d'enfants; real elliptic surfaces Degtyarev, A.; Itenberg, I.; Zvonilov, V., Real trigonal curves and real elliptic surfaces of type I, \textit{J. Reine Angew. Math}.,, \textbf{686}, 221-246, (2014) Topology of real algebraic varieties, Families, moduli of curves (algebraic), Dessins d'enfants theory, Rational and ruled surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations Real trigonal curves and real elliptic surfaces of type I
| 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 holomorphic curve; vector bundle; universal deformation; local moduli space; sheaf cohomology; foliations of complex analytic spaces by curves; complex manifold X. GOMEZ-MONT , Universal families of foliations by curves , Astérisque 150-151, 1987 , p. 109-129. MR 89d:32067 | Zbl 0641.32014 Deformations of submanifolds and subspaces, Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\), Parametrization (Chow and Hilbert schemes), Foliations in differential topology; geometric theory Universal families of foliations by 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 cryptography; finite fields; elliptic curves; authentication; secret sharing; analysis of algorithms Cryptography, Authentication, digital signatures and secret sharing, Finite fields (field-theoretic aspects), Elliptic curves, Analysis of algorithms Threshold ECDSA with an offline recovery party
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli of curves; rational curves with cusps; osculating flag; Schubert cycle; Brill-Noether problem Singularities of curves, local rings, Families, moduli of curves (algebraic), Enumerative problems (combinatorial problems) in algebraic geometry, Rational and unirational varieties, Singularities in algebraic geometry Rational curves with cusps
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; covering of the elliptic curve; Jacobian; Humbert surface; moduli space of principally polarized abelian surfaces; period matrix Murabayashi, N.: The moduli space of curves of genus two covering elliptic curves. Man. Math. 84, 125--133 (1994) Elliptic curves, Families, moduli of curves (algebraic), Algebraic moduli of abelian varieties, classification, Coverings of curves, fundamental group The moduli space of curves of genus two covering elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli of curves; cohomology; stable graphs Families, moduli of curves (algebraic), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Combinatorics of Mumford-Morita-Miller classes in low genus.
| 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 spaces; curves of low genus; plane quartics; Del Pezzo surfaces; configurations of point sets; equivariant cohomology Families, moduli of curves (algebraic), Classical real and complex (co)homology in algebraic geometry, Plane and space curves, Families, moduli, classification: algebraic theory, Configurations and arrangements of linear subspaces Equivariant cohomology of moduli spaces of genus three curves with level two structure
| 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 diagonal cycle; triple product of a pointed curve; regular models; semi-stable reduction; height pairing; \(L\)-functions; modular curve Gross, B. H.; Schoen, C., \textit{the modified diagonal cycle on the triple product of a pointed curve}, Ann. Inst. Fourier (Grenoble), 45, 649-679, (1995) Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Arithmetic ground fields for curves, Modular and Shimura varieties, Algebraic cycles, Arithmetic aspects of modular and Shimura varieties The modified diagonal cycle on the triple product of a pointed 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 function field; bounds for the height of rational points; torsion; canonical height; integral points; elliptic curves Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Heights, Rational points Integral points on elliptic curves over function fields of positive characteristic
| 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 algebraic moduli problems; moduli of vector bundles; vector bundles on surfaces; higher-dimensional varieties and their moduli; vector bundles on curves and their moduli Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic moduli problems, moduli of vector bundles, Vector bundles on curves and their moduli A note on rank two stable bundles over surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves over an algebraic number field; Galois module of \(p\)-torsion points; height conjecture; asymptotic Fermat conjecture; principally polarized abelian variety; curves of genus 2 G. Frey, On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2, in Elliptic curves, modular forms, \& Fermat's last theorem (Hong Kong, 1993), Internat. Press, Cambridge, MA, 1995, pp. 79--98. Elliptic curves over global fields, Elliptic curves On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves degeneration of Hodge structures; algebraic cycles; weight filtration; complex of nearby cycles; local invariant cycle theorem; Chow motives S. Bloch, H. Gillet, and C. Soulé, Algebraic cycles on degenerate fibers, Arithmetic geometry (Cortona, 1994) Sympos. Math., XXXVII, Cambridge Univ. Press, Cambridge, 1997, pp. 45 -- 69. Algebraic cycles, Variation of Hodge structures (algebro-geometric aspects), Motivic cohomology; motivic homotopy theory, (Equivariant) Chow groups and rings; motives Algebraic cycles on degenerate fibers
| 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 Algebraic stacks; Chow rings; stack of rational curves [Ed-Fu1] D. Edidin and D. Fulghesu, The integral Chow ring of the stack of at most 1-nodal rational curves, Comm. Algebra 36 (2008), no. 2, 581--594. (Equivariant) Chow groups and rings; motives, Generalizations (algebraic spaces, stacks), Equivariant homology and cohomology in algebraic topology The integral Chow ring of the stack of at most 1-nodal rational 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 finiteness of Tate-Shafarevich-group; modular elliptic curves Modular and Shimura varieties, Elliptic curves The Kolyvagin papers on Weil 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 surfaces; elliptic curves; Teichmüller space; moduli spaces of flat tori; Veech's foliation; algebraic leaves; complex hyperbolic structure; developing map; elliptic hypergeometric integral; Fuchsian differential equations Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Teichmüller theory for Riemann surfaces, General geometric structures on low-dimensional manifolds, Moduli problems for differential geometric structures, Issues of holonomy in differential geometry, Theta functions and abelian varieties Moduli spaces of flat tori and elliptic hypergeometric functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves irregular surfaces of general type; symmetric products of elliptic curves; bicanonical map of surfaces Polizzi, F., On surfaces of general type with \(p\)\_{}\{g\} = \(q\) = 1, Collect. Math., 56, 181-234, (2005) Surfaces of general type, Families, moduli, classification: algebraic theory On surfaces of general type with \(p_g=q=1\), \(K^2=3\)
| 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 genus four double covers of elliptic curves; rationality of moduli space of elliptic-hyperelliptic curves Bardelli, Fabio; Del Centina, Andrea: The moduli space of genus four double covers of elliptic curves is rational. Pac. J. Math. 144, No. 2, 219-227 (1990) Families, moduli of curves (algebraic), Complete intersections, Algebraic moduli problems, moduli of vector bundles The moduli space of genus four double covers of elliptic curves is rational
| 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 singular fibers; Jacobian elliptic fibrations; Jacobian family of elliptic curves Fibrations, degenerations in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Singularities of curves, local rings, Elliptic curves On the classification of elliptic fibrations with a small number of singular fibres over a base of genus 1
| 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; Chow groups; local fields Algebraic cycles, Elliptic curves over global fields, Elliptic curves over local fields, Abelian varieties of dimension \(> 1\) Divisibility results for 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 rational points; Jacobians; curves of higher genus; descent; Mordell-Weil group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Jacobians, Prym varieties Solving diophantine problems on curves via descent on the Jacobian
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves derived algebraic geometry; elliptic cohomology; Deligne-Mumford moduli stack; \(E_\infty\)-spectra; modular forms; topological modular forms Goerss, Paul G., Topological modular forms [after Hopkins, Miller and Lurie], Astérisque, 332, Exp. No. 1005, viii, 221-255, (2010) Elliptic cohomology, Relations with algebraic geometry and topology, Stacks and moduli problems, Elliptic curves, Bordism and cobordism theories and formal group laws in algebraic topology Topological modular forms [after Hopkins, Miller and Lurie]
| 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 cusp form; Drinfeld module; adele ring; Hecke algebra; classification of elliptic curves; Fourier coefficients; matrix representation of Hecke operators Gekeler E.-U., Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpern, Bonner Math. Schriften 119, Universität Bonn, Bonn 1980. Modular forms associated to Drinfel'd modules, Elliptic curves, Adèle rings and groups, Special algebraic curves and curves of low genus, Holomorphic modular forms of integral weight, Finite ground fields in algebraic geometry, Global ground fields in algebraic geometry Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpern
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves finite fields; pairing-based cryptography; elliptic curves of \(j\)-invariant 1728; Kummer surfaces; rational curves; Weil restriction; isogenies Rational and birational maps, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Effectivity, complexity and computational aspects of algebraic geometry, Isogeny, Elliptic curves Hashing to elliptic curves of \(j\)-invariant 1728
| 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 polysymbol; Massey product; Deligne cohomology Morishita, M; Terashima, Y, Geometry of polysymbols, Math. Res. Lett., 15, 95-115, (2008) Geometric class field theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Symbols and arithmetic (\(K\)-theoretic aspects), Massey products, General theory of differentiable manifolds Geometry of polysymbols
| 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 control theorems; Shimura-Taniyama-Weil conjecture; elliptic curve; modular curve; deformation rings; Hecke algebras; modular Galois representations; moduli spaces of elliptic curves; modular forms; Abelian \(\mathbb{Q}\)-curves Hida, H.: Geometric Modular Forms and Elliptic Curves, 2nd edn. World Scientific, Singapore (2012) Galois representations, Elliptic curves over global fields, Research exposition (monographs, survey articles) pertaining to number theory, \(p\)-adic theory, local fields, Holomorphic modular forms of integral weight, Local ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry Geometric modular forms and elliptic curves
| 0 |
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