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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 derivatives of relative Wronskians; families of Weierstrass points; coarse moduli spaces of curves; Chow classes Gatto L., Trans. Amer. Math. Soc. 351 pp 2233-- (1999) Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), Families, moduli of curves (analytic), Fine and coarse moduli spaces Derivatives of Wronskians with applications to families of special Weierstrass 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 generalization of class field theory; local fields; global fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor Kato, K. : A generalization of class field theory (Japanese) . Sûgaku 40 (1988) 289-311. 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) A 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 Hodge conjecture; limit mixed Hodge structures; cycle class; algebraic Hodge polynomial; nodal curves; moduli space of semi-stable sheaves Transcendental methods, Hodge theory (algebro-geometric aspects), Mixed Hodge theory of singular varieties (complex-analytic aspects), Variation of Hodge structures (algebro-geometric aspects), Period matrices, variation of Hodge structure; degenerations, Algebraic moduli problems, moduli of vector bundles, Fine and coarse moduli spaces, Structure of families (Picard-Lefschetz, monodromy, etc.) Hodge conjecture for the moduli space of semi-stable sheaves over a nodal 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 torsion algebraic cycles; Chow group; cycle map; rational classes of codimension 2 Saito, S.: On the cycle map for torsion algebraic cycles of codimension two. Invent. Math. 106(3), 443--460 (1991) Algebraic cycles, Parametrization (Chow and Hilbert schemes) On the cycle map for torsion algebraic cycles of codimension 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 number of points on elliptic curves; finite fields Curves over finite and local fields, Finite ground fields in algebraic geometry The number of points on elliptic curves \(E\colon y^ 2=x^ 3+cx\) over \(\mathbb F_ p\bmod 8\).
| 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 modular elliptic curves; order of vanishing; Artin \(L\)-functions; Dirichlet \(L\)-functions V. KUMAR MURTY , Non-Vanishing of L-Functions and their Derivatives , in Automorphic Forms and Analytic Number Theory, R. MURTY Ed., pp. 89-113, Centre de Recherches Mathématiques, 1990 . Zbl 0745.11033 \(L\)-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 over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, \(\zeta (s)\) and \(L(s, \chi)\), Other Dirichlet series and zeta functions Non-vanishing of \(L\)-functions and their derivatives
| 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 genus; formal group laws associated to supersingular elliptic curves; Jacobi quartics; Legendre polynomials; elliptic curves of Weierstrass forms; discriminant Landweber, P.S.: Supersingular Elliptic Curves and Congruences for Legendre Polynomials. In: Landweber, P.S. (ed.) Elliptic Curves and Modular Forms in Topology. Proceedings, Princeton 1986. (Lect. Notes Math., vol. 1326, pp. 69--93) Berlin Heidelberg New York: Springer 1988 Formal groups, \(p\)-divisible groups, Spherical harmonics, Special algebraic curves and curves of low genus, Elliptic curves Supersingular elliptic curves and congruences for Legendre polynomials
| 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 imaginary quadratic field; Selmer\(groups\); Weil curve; Heegner points; conjecture of Birch and Swinnerton-Dyer Special algebraic curves and curves of low genus, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Rational points, Elliptic curves, Quadratic extensions Rational points of infinite order 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 factors of division polynomials; Schoof's algorithm; number of rational points; elliptic curve; prime field; modular curves Morain, J. Théor. Nombres Bordeaux 7 pp 255-- (1995) Curves over finite and local fields, Computational aspects of algebraic curves, Holomorphic modular forms of integral weight, Number-theoretic algorithms; complexity Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves families of elliptic curves; rational point; indivisible points; height functions R. Gupta and K. Ramsay, Indivisible points on families of elliptic curves , J. Num. Theor. 63 (1997), 357-372. Elliptic curves over global fields, Elliptic curves, Rational points Indivisible points on 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 torsion in elliptic curves; fine moduli space; coarse moduli space; number of cusps; number of elliptic points Cox, David A.; Parry, Walter R., Torsion in elliptic curves over \(k(t)\), Compos. Math., 41, 3, 337-354, (1980) Elliptic curves, Elliptic curves over global fields, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves, Families, moduli of curves (algebraic), Fine and coarse moduli spaces, Algebraic moduli problems, moduli of vector bundles, Enumerative problems (combinatorial problems) in algebraic geometry Torsion in elliptic curves over \(k(t)\)
| 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 family of elliptic curves; Weierstraß form; lifted \(p\)-adic homology; zeta endomorphism \(p\)-adic cohomology, crystalline cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves A \(p\)-adic cohomological method for the Weierstrass family and its zeta invariants
| 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 theory; algebraic fundamental groups; finite simple group; wreath product; Galois group; unramified covering of the affine line; group enlargements; enlargements; tame fundamental groups of curves Abhyankar, S. S.: Group enlargements. CR acad. Sci. Paris 312, 763-768 (1991) Extensions, wreath products, and other compositions of groups, Plane and space curves, Separable extensions, Galois theory Group enlargements
| 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 fibration; Hirzebruch-Jung strings; birational transformation; Euler characteristic of a three-dimensional elliptic fibration Grassi, A., The singularities of the parameter surface of a minimal elliptic threefold, Internat. J. Math., 4, 203, (1993) \(3\)-folds, Singularities of surfaces or higher-dimensional varieties, Structure of families (Picard-Lefschetz, monodromy, etc.) The singularities of the parameter surface of a minimal elliptic threefold
| 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 geometric invariant theory; moduli of curves; curves of genus four; intersection cohomology Geometric invariant theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Families, moduli of curves (algebraic) Cohomology of the moduli space of non-hyperelliptic genus four 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 quadratic twists of elliptic curves; modular forms; \(\mathbb{F}_ p\)-rational points; special values of \(L\)-functions; cubic twists Ono, K, Twists of elliptic curves, Compos. Math., 106, 349-360, (1997) Elliptic curves over global fields, Elliptic curves, Rational points Twists 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 Galois cohomology; number fields; elliptic curves; abelian varieties; function fields; profinite groups; class field theory; formal groups; Milnor K-groups; Lubi-Tate groups Collected or selected works; reprintings or translations of classics, History of number theory, History of algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic problems in algebraic geometry; Diophantine geometry, Abelian varieties and schemes Collected works of John Tate. Part I (1951--1975). Edited by Barry Mazur and Jean-Pierre Serre
| 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 zero cycles; Bloch conjecture; Albanese variety; Chow group; pushout diagram; 1-motive; Chern classes in Deligne cohomology H. Gillet, On the \(K\)-theory of surfaces with multiple curves and a conjecture of Bloch , Duke Math. J. 51 (1984), no. 1, 195-233. Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles On the K-theory of surfaces with multiple curves and a conjecture of Bloch
| 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 Jacobians; moduli of curves; double ramification cycle Jacobians, Prym varieties, Picard schemes, higher Jacobians, Algebraic moduli problems, moduli of vector bundles Extending the double ramification cycle using Jacobians
| 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 finite fields; discrete elliptic logarithm function; public key cryptosystems; twisted pair of curves Cryptography, Elliptic curves, Arithmetic ground fields for curves On implementing elliptic curve cryptosystems
| 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 supersymmetric product of supercurve; supercurve; superdivisor; fermions; SUSY-curves Pérez, J. A. Domínguez; Ruipérez, D. Hernández; De Salas, C. Sancho: The variety of positive superdivisors of a supercurve (supervortices). J. geom. Phys. 12, 183-203 (1993) Noncommutative algebraic geometry, Curves in algebraic geometry, Supervarieties The variety of positive superdivisors of a supercurve (supervortices)
| 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 analogue of the theory of elliptic modular curves; Drinfeld modules; Drinfeld's upper half-plane; expansions at the cusps of certain modular forms; Manin-Drinfeld theorem; algebraic modular forms; jacobian Ernst-Ulrich Gekeler, Drinfel\(^{\prime}\)d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 1986. Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for curves, Modular forms associated to Drinfel'd modules, Global ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic theory of algebraic function fields Drinfeld 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 moduli of stable bundles; elliptic fibre bundles; compact Riemann surface; cohomology; graph method; elliptic Hopf surfaces Teleman, A, Moduli spaces of stable bundles on non-Kähler elliptic fibre bundles over curves, Expo. Math., 16, 193-248, (1998) Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Algebraic moduli problems, moduli of vector bundles Moduli spaces of stable bundles on non-Kählerian elliptic fibre bundles over 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 Dwork-Siegel conjecture; differential equations for G-functions; Picard- Fuchs equations; Padé approximations; accessory parameters; transcendence; elliptic curves; continued fractions; fast computation of \(\pi \) D.V. Chudnovsky and G.V. Chudnovsky. Computational problems in arithmetic of linear differential equations. Some Diophantine applications. Number theory (New York, 1985/1988), 12--49, Lecture Notes in Math., 1383, Springer, Berlin (1989). Transcendence (general theory), Continued fractions and generalizations, Complex multiplication and abelian varieties, Ordinary differential equations in the complex domain, Research exposition (monographs, survey articles) pertaining to number theory, Padé approximation Computational problems in arithmetic of linear differential equations. Some diophantine applications
| 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 cuspidal divisor class group; group of modular units; modular; curves; congruence subgroups; Jacobian; cuspidal groups; arithmetic of special values of L-functions; weight two Eisenstein series; congruence formulae Glenn Stevens, The cuspidal group and special values of \(L\)-functions, Trans. Am. Math. Soc.291 (1985), p. 519-550 Holomorphic modular forms of integral weight, Congruences for modular and \(p\)-adic modular forms, Jacobians, Prym varieties The cuspidal group and special values of L-functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves twenty seven lines of cubic surface; real cubics; elliptic and hyperbolic lines; projective space; orientable manifold; relative orientation; enumerative geometry; cohomology classes; vector bundles; sphere bundles; sections; Euler class; degree of map; multiplicity of zero; Welschinger invariant C. Okonek, A. Teleman, Intrinsic signs and lower bounds in real algebraic geometry. J. für die reine angew. Math (Crelles Journal) 2014(688), 219--241 (2012) Real algebraic sets, Enumerative problems (combinatorial problems) in algebraic geometry, Sphere bundles and vector bundles in algebraic topology Intrinsic signs and lower bounds in real 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 elliptic curves; K-theory; zeta functions; higher regulators S. Bloch, \textit{Higher regulators, algebraic K- theory and zeta functions of elliptic curves}, Volume 11 of CRM Monograph Series, AMS, Providence, RI, U.S.A. (2000). Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Computations of higher \(K\)-theory of rings, Research exposition (monographs, survey articles) pertaining to \(K\)-theory, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture Higher regulators, algebraic \(K\)-theory, and zeta functions of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; cohomological field theories; quantum integrable systems; double ramification cycle Kim, H.-C., Kim, S.: M5-branes from gauge theories on the 5-sphere. J. High Energy Phys. \textbf{2013}, 144 (2013). 10.1007/JHEP05(2013)144 Families, moduli of curves (algebraic), Relationships between algebraic curves and integrable systems, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Groups and algebras in quantum theory and relations with integrable systems Double ramification cycles and quantum integrable systems
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves motivic homotopy; Koras-Russell threefolds; equivariant \(K\)-theory; higher Chow groups; motivic cohomology Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Stable homotopy theory, spectra, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) \(\mathbb{A}^1\)-contractibility of Koras-Russell threefolds
| 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-Poincaré formula; rigid analytic curves; adic space; valuation of higher rank; Artin representation; Swan representation; Lefschetz fixed point formula Huber, R.: Swan representations associated with rigid analytic curves. Journal für die Reine und Angewandte Mathematik \textbf{537}, 165-234 (2001) Rigid analytic geometry, Arithmetic ground fields for curves, Étale and other Grothendieck topologies and (co)homologies, Ramification and extension theory Swan representations associated with rigid analytic 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 exponential height; diophantine equations; Bogomolov-Miyaoka-Yau inequality; arithmetic surface; Arakelov's intersection theory; intersection numbers; Szpiro conjecture; Parshin trick; asymptotic Fermat theorem; boundedness of the torsion of elliptic curves A. N. Parshin, ``The Bogomolov -- Miyaoka -- Yau inequality for the arithmetical surfaces and its applications'', Seḿinaire de theórie des nombres (Paris, 1986 -- 87), Progr. Math., 75, Birkhaüser, Boston, MA, 1988, 299 -- 312 Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Arithmetic ground fields for surfaces or higher-dimensional varieties, Cubic and quartic Diophantine equations The Bogomolov-Miyaoka-Yau inequality for the arithmetical surfaces and its applications
| 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 Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. Elliptic curves, Rational points, Elliptic curves over local fields, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 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 sixth Painlevé transcendent; algebraic solutions; algebraic curves of higher genera; uniformization by theta-functions Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Painlevé-type functions, Relationships between algebraic curves and integrable systems, Special algebraic curves and curves of low genus, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain The sixth Painlevé transcendent and uniformizable orbifolds
| 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 Atiyah-Segal map; Riemann-Roch transformation; Grothendieck-Riemann-Roch theorem; Deligne-Mumford stack; quotient stack; inertia stack; equivariant $K$-theory; higher Chow groups; coarse moduli space map; Morita isomorphism; Köck's conjecture Riemann-Roch theorems, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), \(K\)-theory of schemes Atiyah-Segal theorem for Deligne-Mumford stacks and applications
| 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 cycle; elliptic curves Cycles and subschemes, Special algebraic curves and curves of low genus, Algebraic theory of abelian varieties, Elliptic curves Rational cycles on Abelian varieties. IV
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Calabi-Yau varieties; families of elliptic curves; elliptically (chain) connected varieties Calabi-Yau manifolds (algebro-geometric aspects), Families, moduli of curves (algebraic) Maps from K-trivial varieties and connectedness problems
| 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 twists of elliptic curves; heights Lang, S.: Conjectured diophantine estimates on elliptic curves, arithmetic and geometry, vol. I, Progr. Math., vol. 35, Birkhäuser, Boston, pp. 155-171 (1983) Heights, Elliptic curves over global fields, Rational points Height of rational points on quadratic twists of a given 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 nef cone; symmetric product of curves Bastianelli, F., Remarks on the nef cone on symmetric products of curves, Manuscripta Math., 130, 113-120, (2009) Divisors, linear systems, invertible sheaves, Families, moduli of curves (algebraic), Computational aspects of algebraic surfaces Remarks on the nef cone on symmetric products of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves finite field; elliptic curve; Jacobian of curves Schmoyer, S. L., The triviality and nontriviality of Tate-lichtenbaum self-pairings on Jacobians of curves, (2006) Curves over finite and local fields, Elliptic curves The triviality and nontriviality of Tate-Lichtenbaum self pairings on Jacobians of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic completely integrable systems; Poisson geometry; integrable Hamiltonian systems; symmetric product of curves; Hénon-Heiles hierarchy Vanhaecke, P., Integrable Systems and Symmetric Products of Curves, Math. Z., 1998, vol. 227, no. 1, pp. 93--127. Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Analytic theory of abelian varieties; abelian integrals and differentials Integrable systems and symmetric products of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; Deligne-Mumford compactification; divisor Families, moduli of curves (algebraic) Boundary complexes of moduli spaces of curves in higher 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 Abel-Jacobi map; higher Chow group; regulator map; absolute Hodge cohomology Kerr M. and Lewis J.\ D., The Abel-Jacobi map for higher Chow groups, II, Invent. Math. 170 (2007), no. 2, 355-420. Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) The Abel-Jacobi map for higher Chow groups. 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 algebraic families of curves; Faltings' theorem; Mordell conjecture; projective variety; Szpiro constants; elliptic curve De Diego, Teresa: Théorème de faltings (conjecture de Mordell) pour LES familles algébriques de courbes, C. R. Acad. sci. Paris sér. I math. 323, No. 2, 175-178 (1996) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Families, moduli of curves (algebraic), Rational points, Arithmetic ground fields for curves Faltings' theorem (Mordell's conjecture) for algebraic families of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Steenrod algebras; cohomology of groups; characteristic classes; algorithms; computation; Chow rings; cohomology rings; Stiefel-Whitney classes; Steenrod operations Cohomology of groups, Homology of classifying spaces and characteristic classes in algebraic topology, Steenrod algebra, Characteristic classes and numbers in differential topology, (Equivariant) Chow groups and rings; motives The computation of Stiefel-Whitney 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 Kummer surface; Brauer group; rational points; torsion of elliptic curves A.N. Skorobogatov, Yu.G. Zarhin, The Brauer group of Kummer surfaces and torsion of elliptic curves, J. Reine Angew. Math. 666, 115-140 (2012) \(K3\) surfaces and Enriques surfaces, Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties The Brauer group of Kummer surfaces and torsion 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 generalized Hamming weight; weight distribution; trace codes; fibre product of Artin-Schreier curves; rational points; supersingular curves van der Geer G., van der Vlugt M.: Fibre products of Artin--Schreier curves and generalized Hamming weights of codes. J. Combin. Theory Ser. A 70, 337--348 (1995) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic ground fields for curves Fibre products of Artin-Schreier curves and generalized Hamming weights of codes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher Chow groups; category of mixed motives; exact faithful functor; mixed Hodge structures; Albanese map Asakura, M.: Motives and algebraic de Rham cohomology. The arithmetic and geometry of algebraic cycles, Proceedings of the CRM Summer School. CRM Proc. Lect. Notes \textbf{24}, 133-155 (2000) Motivic cohomology; motivic homotopy theory, de Rham cohomology and algebraic geometry, Transcendental methods, Hodge theory (algebro-geometric aspects), Sheaves of differential operators and their modules, \(D\)-modules, (Equivariant) Chow groups and rings; motives Motives and algebraic de Rham 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 Chow-motif of the Severi-Brauer variety; cohomology groups Karpenko, N.A.: Grothendieck Chow motives of Severi--Brauer varieties (Russian). Algebra Anal. 7(4), 196--213 (1995) (transl. in St. Petersbg. Math. J. 7(4), 649--661 (1996)) Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(K\)-theory of schemes, Generalizations (algebraic spaces, stacks), Parametrization (Chow and Hilbert schemes) The Grothendieck Chow-motifs of Severi-Brauer 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 motive; motivic cohomology; Chow groups; numerical equivalence of cycles (Equivariant) Chow groups and rings; motives, Algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Motivic cohomology; motivic homotopy theory On isotropic and numerical equivalence of 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 \(p\)-division representations; elliptic curves; complex multiplication; integers of an imaginary quadratic field; rational primes Boston, N.; Ullom, S. V.: Representations related to CM elliptic curves. Math. proc. Cambridge philos. Soc. 113, 71-85 (1993) Elliptic curves, Complex multiplication and abelian varieties, Rational points, Complex multiplication and moduli of abelian varieties, Quadratic extensions, Elliptic curves over global fields Representations related to 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 unramified extensions; division points; class numbers; class field towers of infinite degree; semi-stable elliptic curves Class field theory, Iwasawa theory, Elliptic curves, Ramification and extension theory Some results on class numbers and unramified extensions of 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 rank of elliptic curves; theorem of Lutz-Nagel; \(2\)-descent; families of elliptic curves; arithmetic function; quartic diophantine equation Elliptic curves over global fields, Other results on the distribution of values or the characterization of arithmetic functions, Elliptic curves Families of elliptic curves of rank \(\geq 1\) and remarks on an arithmetic function associated to an algorithm of 2-descent of Tate
| 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 three; real multiplication; abelian variety Hoffman, J. W.; Wang, H.: 7-gons and genus 3 hyperelliptic curves. Rev. R. Acad. cienc. Exactas fís. Nat., ser. A mat. 107, 35-52 (2013) Abelian varieties of dimension \(> 1\), Complex multiplication and moduli of abelian varieties, Special algebraic curves and curves of low genus 7-gons and genus three 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 Goldwasser-Kilian-Atkin method; primes of over 1000 digits; elliptic curves; primality Morain, F.: Elliptic curves, primality proving and some titanic primes. Astérisque 198--200, 245-251 (1992) Number-theoretic algorithms; complexity, Primality, Factorization; primality, Elliptic curves Elliptic curves, primality proving, and some Titanic primes
| 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 configuration space; Hodge structure; mixed Hodge module; moduli space of elliptic curves Ayala, D., Francis, J.: Poincaré/Koszul duality (2014). arXiv:1409.2478 Variation of Hodge structures (algebro-geometric aspects), Families, moduli of curves (algebraic), Automorphic forms, one variable Resolving mixed Hodge modules on configuration spaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves derived category of motives; Chow group; motivic cohomology; mixed Tate motive; adjoint functor Motivic cohomology; motivic homotopy theory, (Equivariant) Chow groups and rings; motives Adjoint functors on the derived category of 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 mixed motives; Hodge conjecture; Hodge structure of geometric origin; Chow groups; cycle class map; correspondence Transcendental methods, Hodge theory (algebro-geometric aspects), Generalizations (algebraic spaces, stacks), Algebraic cycles, Rational and birational maps Hodge conjecture and mixed motives. 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 minimally elliptic surface; fundamental cycle on the minimal resolution; Auslander-Reiten quivers of reflexive modules Kahn C.P., Reflexive modules on minimally elliptic singularities, Math. Ann., 1989, 285(1), 141--160 Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Representation theory of associative rings and algebras, Modifications; resolution of singularities (complex-analytic aspects), Elliptic surfaces, elliptic or Calabi-Yau fibrations Reflexive modules on minimally elliptic singularities
| 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 functions; arithmetical exceptionality; exceptionality of permutation groups; elliptic curves; monodromy groups Guralnick, R. M.; Müller, P.; Saxl, J., The rational function analogue of a question of Schur and exceptionality of permutation representations, \textit{Mem. Amer. Math. Soc.}, 162, 773, viii+79, (2003) Field arithmetic, Elliptic curves over global fields, Arithmetic ground fields for curves, Coverings of curves, fundamental group, Primitive groups, Research exposition (monographs, survey articles) pertaining to field theory The rational function analogue of a question of Schur and exceptionality of permutation 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 discrete logarithm problem; elliptic curve; abelian group of points; taking logarithms by division by two Bessalov, A.V., A method of solution of the problem of taking the discrete logarithm on an elliptic curve by division of points by two, Cybern. Syst. Anal., 37, 820-823, (2001) Cryptography, Applications to coding theory and cryptography of arithmetic geometry A method of solution of the problem of taking the discrete logarithm on an elliptic curve by division of points by 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 modular invariance; tensor product; Virasoro modules; central charge; elliptic curves Virasoro and related algebras, Elliptic curves, Relationship to Lie algebras and finite simple groups, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Modular invariant Virasoro modules and elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves self-intersection of dualizing sheaves; elliptic curves; Arakelov theory; Arakelov-Green function; Frey curves; genus; Néron-Tate height; Jacobian Szpiro, L. 1990.Sur les propriétés numériques du dualisant relatif d'une surface arithmétique, The Grothendieck Festschrift Vol. III, 229--246. Boston: Birkhäuser. Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Sur les propriétés numériques du dualisant relatif d'une surface arithmétique. (On the numerical properties of the relative dualizing sheaf of an arithmetic surface)
| 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 Tate-Shafarevich group; elliptic curves; evidence for the truth of the Birch and Swinnerton-Dyer conjecture; ideal class annihilators Rubin, K.: Tate-Shafarevich groups and
\[
L
\]
-functions of elliptic curves with complex multiplication. Invent. Math. 89, 527--560 (1987) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Complex multiplication and abelian varieties, Special algebraic curves and curves of low genus, Rational points, Elliptic curves Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Green's functions; Chow groups; elliptic curves; complex multiplication; Abel-Jacobi maps Mellit, A.: Higher Green's functions for modular forms. Ph. D. thesis, Rheinische Friedrich-Wilhelms-Universität Bonn (2008) Research exposition (monographs, survey articles) pertaining to number theory, Holomorphic modular forms of integral weight, Complex multiplication and moduli of abelian varieties, Algebraic cycles Higher Green's functions for modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic curves; Riemann surfaces; moduli spaces; cohomology rings; Chow rings; divisor classes; homology groups; Picard groups; Teichmüller theory; Gysin spectral sequence Arbarello E., Grundlehren der Mathematischen Wissenschaften 268, in: Geometry of Algebraic Curves (2010) Families, moduli of curves (algebraic), (Equivariant) Chow groups and rings; motives, Divisors, linear systems, invertible sheaves, Picard groups, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Teichmüller theory for Riemann surfaces Divisors in the moduli spaces of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves quadratic forms; representation of integers; generalized Weil hypothesis; elliptic curves with complex multiplication; method of ascent; modular forms; functional equations B. T. Tashpulatov and L. A. Kogan, Representation of Integers by Quadratic Forms [in Russian], Fan, Tashkent (1993). Sums of squares and representations by other particular quadratic forms, Research exposition (monographs, survey articles) pertaining to number theory, Theta series; Weil representation; theta correspondences, Quadratic forms over global rings and fields, Theta functions and abelian varieties, Elliptic functions and integrals Representation of numbers by quadratic forms.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves cryptography; endomorphism of elliptic curves; Frobenius endomorphism Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry Endomorphisms on elliptic curves for optimal subspaces and applications to differential equations and nonlinear 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 Murre's conjecture; motivic decomposition; Chow group; curve; abelian variety; elliptic modular threefold; product varieties Xu, K; Xu, Z, Remarks on murre's conjecture on Chow groups, J. K-Theo., 12, 3-14, (2013) (Equivariant) Chow groups and rings; motives, Algebraic cycles Remarks on Murre's conjecture on 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 moduli space of curves; effective cone; higher codimension cycles; extremal rays Families, moduli of curves (algebraic), Algebraic cycles, Minimal model program (Mori theory, extremal rays) On the effective cone of higher codimension cycles in \(\overline{\mathcal{M}}_{g,n} \)
| 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 moduli spaces of curves; algebraic curves over global fields; discriminantal varieties; cohomology rings; Hodge structures Bergstrom, J.; Tommasi, O., The rational cohomology of M\_{}\{4\}, Math. Ann., 338, 207, (2007) Families, moduli of curves (algebraic), Curves over finite and local fields, Discriminantal varieties and configuration spaces in algebraic topology, Arithmetic ground fields for curves, Transcendental methods, Hodge theory (algebro-geometric aspects), Topological properties in algebraic geometry The rational cohomology of \(\overline{\mathcal{M}}_4\)
| 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 construction of high-rank elliptic curves; Mordell-Weil group K. Nagao, Construction of high-rank elliptic curves, Kobe J. Math,11 (1994), 211--219. Elliptic curves over global fields, Elliptic curves Construction of high-rank 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 function field of elliptic curve; Witt ring; elliptic curve; generators; relations; symmetric bilinear spaces; cohomological invariants; Grothendieck ring; étale cohomology groups Arason, J. K.; Elman, R.; Jacob, B.: On the Witt ring of elliptic curves, Proc. symp. Pure math. 58, No. Part II, 1-25 (1995) Algebraic theory of quadratic forms; Witt groups and rings, Elliptic curves, Étale and other Grothendieck topologies and (co)homologies, Other nonalgebraically closed ground fields in algebraic geometry, Vector bundles on curves and their moduli On the Witt ring 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 free resolutions over the exterior algebra; cohomology of sheaves; Chow form D. Eisenbud, Computation of cohomology, in: W.V. Vasconcelos et al. (Eds.), Computational Methods in Commutative Algebra and Algebraic Geometry, Springer, New York, 1997, pp. 209--216. Exterior algebra, Grassmann algebras, Syzygies, resolutions, complexes and commutative rings An exterior view of modules and 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 moduli space of curves; mapping class group; level structures; Picard group; Torelli group; group cohomology Ivanov, N. V.: Subgroups of Teichmüller modular groups. Translations of Mathematical Monographs \textbf{115}. AMS (1992) Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Picard groups, General geometric structures on low-dimensional manifolds The second rational homology group of the moduli space of curves with level 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 triangulated category of effective motivic complexes; algebraic cycle cohomology; motivic cohomology theory Voevodsky, V., \textit{triangulated categories of motives over a field}, Cycles, transfers, and motivic homology theories, 188-238, (2000), Princeton University Press, Princeton, NJ Motivic cohomology; motivic homotopy theory, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Triangulated categories of motives over a 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 Moduli of curves; elliptic curves; riemann surfaces; orblfods R. Hain, \textit{Lectures on moduli spaces of elliptic curves}, in \textit{Transformation groups and moduli spaces of curves}, L. Ji and S.-T. Yau eds., \textit{Adv. Lect. Math.}\textbf{16}, International Press, U.S.A. (2011), pg. 95 [arXiv:0812.1803]. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Elliptic curves, Moduli, classification: analytic theory; relations with modular forms, Stacks and moduli problems, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Topology and geometry of orbifolds Lectures on moduli spaces 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 Singularities; elliptic functions; modular curves; characteristic of a curve; modular equations Curves in algebraic geometry, Singularities in algebraic geometry, Elliptic functions and integrals On the singularities of the modular equations and 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-dimensional algebraic varieties; birational geometry; birational classification theory; minimal model program; Mori theory; cohomological vanishing theorems; cohomological nonvanishing theorems; Cartier divisors; morphisms from curves; varieties with many rational curves; rational quotient of a variety; cone theorem; contraction theorem; extremal rays Debarre O., Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, New York 2001. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Surfaces and higher-dimensional varieties, Minimal model program (Mori theory, extremal rays), Divisors, linear systems, invertible sheaves Higher-dimensional 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 nongap sequence of a Weierstrass point; coverings of elliptic curves E. Ballico, C. Keem, Weierstrass multiple points on algebraic curves and ramified coverings, Israel. J. Math. Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, Vector bundles on curves and their moduli Weierstrass multiple points on algebraic curves and ramified coverings
| 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 Complex semisimple group; quantized enveloping algebra at a root of unity; cohomology; tilting module; principal block; support; two-sided cell; affine Weyl group; nilpotent cone; Springer resolution; equivariant coherent sheaf; orbit; equivariant vector bundle Bezrukavnikov, Roman, Cohomology of tilting modules over quantum groups and \(t\)-structures on derived categories of coherent sheaves, Invent. Math., 166, 2, 327-357, (2006) Quantum groups (quantized enveloping algebras) and related deformations, Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) Cohomology of tilting modules over quantum groups and \(t\)-structures on derived categories of coherent 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 torsion Galois modules; mod \(p\) representations; infinite families of modular elliptic curves; complex multiplication Rubin, K. and Silverberg, A., Families of elliptic curves with constant mod~{\(p\)} representations, Elliptic Curves, Modular Forms, \& {F}ermat's Last Theorem ({H}ong {K}ong, 1993), Ser. Number Theory,~I, 148-161, 1363500, (1995), Int. Press, Cambridge, MA Elliptic curves over global fields, Elliptic curves, Holomorphic modular forms of integral weight Families of elliptic curves with constant \(\text{mod }p\) 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 survey articles (algebraic geometry); stacks; Artin stacks; moduli of vector bundles; curves over arithmetic ground fields; cohomology of algebraic stacks; Weil conjectures F. Neumann, Algebraic stacks and moduli of vector bundles, Publicações Matemáticas do IMPA , Colóquio Brasileiro de Matemática, 27, 2009. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Generalizations (algebraic spaces, stacks), Algebraic moduli problems, moduli of vector bundles, \(p\)-adic cohomology, crystalline cohomology, Arithmetic ground fields for curves, Vector bundles on curves and their moduli Algebraic stacks and moduli of vector bundles. Paper from the 27th Brazilian Mathematics Colloquium -- 27\(\degree\) Colóquio Brasileiro de Matemática, Rio de Janeiro, Brazil, July 27--31, 2009
| 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 cubic residue symbol and cubic roots; hashing to ordinary elliptic curves of \(j\)-invariant 0; indifferentiability from a random oracle; pairing-based cryptography Applications to coding theory and cryptography of arithmetic geometry, Elliptic curves, Effectivity, complexity and computational aspects of algebraic geometry Indifferentiable hashing to ordinary elliptic \(\mathbb{F}_{q} \)-curves of \(j=0\) with the cost of one exponentiation in \(\mathbb{F}_{q} \)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves conformal blocks; moduli space of stable pointed rational curves; Chow quotient; GIT quotient; weighted pointed stable curves; Gale duality Giansiracusa, N., Conformal blocks and rational normal curves, J. Algebraic Geom., 22, 4, 773-793, (2013) Families, moduli of curves (algebraic), Geometric invariant theory, Parametrization (Chow and Hilbert schemes) Conformal blocks and rational normal 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 weighted projective lines of genus one; tubular mutations; exceptional indecomposable vector bundles; distinguished triangles; elliptic curves; categories of graded coherent sheaves; derived categories; natural transformations H. Meltzer, Tubular mutations, Colloq. Math., 74 (1997), no. 2, 267--274. Zbl 0886.16013 MR 1477569 Representations of orders, lattices, algebras over commutative rings, Vector bundles on curves and their moduli, Module categories in associative algebras Tubular mutations
| 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 decomposition of diagonal; Calabi-Yau complete intersection; decomposable 0-cycle; Chow ring; intersection theory; Hodge structure Fu, L, Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections, Adv. Math., 244, 894-924, (2013) Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), (Equivariant) Chow groups and rings; motives, Projective and enumerative algebraic geometry Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections
| 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 tropical geometry; moduli spaces of curves; matroid; Chow ring Families, moduli of curves (algebraic), Geometric aspects of tropical varieties, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Combinatorial aspects of matroids and geometric lattices, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Chow rings of heavy/light Hassett spaces via tropical 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 noncommutative algebraic geometry; elliptic curves; quotients of Stein varieties; category of coherent sheaves; Rieffel's theorem; non-Archimedean quantum tori Yan Soibelman and Vadim Vologodsky, Noncommutative compactifications and elliptic curves, Int. Math. Res. Not. 28 (2003), 1549 -- 1569. Noncommutative algebraic geometry, Elliptic curves, Noncommutative geometry (à la Connes) Noncommutative compactifications and elliptic curves.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; Tate-Shafarevich groups; Selmer groups; modules of cofinite type; distributions; alternating matrix Bhargava, Manjul; Kane, Daniel M.; Lenstra,, Hendrik W., Jr.; Poonen, Bjorn; Rains, Eric, Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves, Camb. J. Math., 2168-0930, 3, 3, 275\textendash 321 pp., (2015) Elliptic curves, Elliptic curves over global fields, Finite ground fields in algebraic geometry Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups 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 logarithmic de Rham complex; vanishing theorems; Deligne theory of mixed Hodge structures; Moishežon manifold; local free sheaves; cohomology; holomorphic covariant derivations with poles H. Esnault and E. Viehweg, Logarithmic de Rham complexes and vanishing theorems, Invent. Math. 86 (1986), 161-194. Complex manifolds, Analytic sheaves and cohomology groups, Sheaves and cohomology of sections of holomorphic vector bundles, general results, Vanishing theorems Logarithmic de Rham complexes and vanishing theorems
| 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 Yang--Baxter equations; vector bundles on genus one curves; elliptic fibrations; derived categories of sheaves; Massey products Burban, I., Kreußler, B., Vector bundles on degenerations of elliptic curves and Yang-Baxter equations. Mem. Amer. Math. Soc. 220, no. 1035 (2012) Vector bundles on curves and their moduli, Elliptic curves, Yang-Baxter equations Vector bundles on degenerations of elliptic curves and Yang-Baxter
| 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 Geometry of elliptic curves Elliptic curves A geometrical illustration of the cubic transformation in elliptic 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 formal group law; generalized cohomology theory; elliptic curves M. Bakuradze and M. Jibladze, ''Some explicit expressions concerning BP,'' arXiv: 1310.0783v2 [math.AT]. Bordism and cobordism theories and formal group laws in algebraic topology, Formal power series rings, Elliptic curves, Generalized (extraordinary) homology and cohomology theories in algebraic topology Some explicit expressions concerning BP
| 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; excess linear series; secant bundle; secant space to a curve; symmetric product of a curve \textsc{M. Aprodu and E. Sernesi,} Excess dimension for secant loci in symmetric products of curves, E. Collect. Math. (2016). 10.1007/s13348-016-0166-2. Special divisors on curves (gonality, Brill-Noether theory), Plane and space curves, Determinantal varieties Excess dimension for secant loci in symmetric products of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves prescribed j-invariants of elliptic curves Comalada, Salvador; Nart, Enric: Modular invariant and good reduction of elliptic curves. Math. ann. 293, No. 2, 331-342 (1992) Arithmetic ground fields for curves, Algebraic number theory: global fields, Elliptic curves Modular invariant and good reduction 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 face angles of tetrahedra; division of sphere surfaces; homogen consisted space figures; congruent space divisions; non-euclidean measurement; group theoretical considerations of two-dimensional spaces; group theoretical considerations of three-dimensional hyperbolic spaces Elliptic surfaces, elliptic or Calabi-Yau fibrations, \(3\)-folds, Classical groups (algebro-geometric aspects), Polyhedra and polytopes; regular figures, division of spaces, Three-dimensional polytopes, Surfaces in Euclidean and related spaces, Geometric quantization On the division of a space by elliptical measurement.
| 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 Special algebraic curves and curves of low genus, Cycles and subschemes Extremality of loci of hyperelliptic curves with marked Weierstrass 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 depth of tensor product; vanishing of local cohomology; vector bundle; hypersurface domain; \(S_{r+1}\) Huneke C. and Wiegand R. (1997). Tensor products of modules, rigidity and local cohomology. Math. Scan. 81: 161--183 Local cohomology and commutative rings, Dimension theory, depth, related commutative rings (catenary, etc.), Vanishing theorems in algebraic geometry Tensor products of modules, rigidity and local 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 p-ordinary CM types; motives; period relation; Hodge-Tate decompositions of the cohomology of an abelian variety; with complex multiplications; Hodge conjecture; p-adic periods of the quotients of Fermat curves; Hodge-Tate decompositions of the cohomology of an abelian variety with complex multiplications [39] Ehud de Shalit, &On monomial relations between \(p\)-adic periods&#xJ. Reine Angew. Math.374 (1987), p.~193-MR~8 | &Zbl~0597. Complex multiplication and abelian varieties, Local ground fields in algebraic geometry, Period matrices, variation of Hodge structure; degenerations, Special algebraic curves and curves of low genus, Generalizations (algebraic spaces, stacks), Transcendental methods, Hodge theory (algebro-geometric aspects), Arithmetic ground fields for abelian varieties On monomial relations between p-adic periods
| 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 covering of stable genus three curves; fibre of Prym map; abelian surface; symmetric theta divisor; Satake compactification of the moduli space of principally polarized abelian surfaces Verra, A.: The fiber of the Prym map in genus 3. Math. Ann. 276, 433--448 (1987) Algebraic moduli of abelian varieties, classification, Families, moduli of curves (algebraic), Theta functions and abelian varieties The fibre of the Prym map in genus three
| 0 |
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