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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 positive definiteness; positive definite extendibility; polar decomposition; characterizations of subnormality; complex moment problem on real algebraic curves; two-dimensional real moment problem; real algebraic sets J. Stochel and F. H. Szafraniec, \textit{The complex moment problem and subnormality: A polar decomposition approach}, J. Funct. Anal., 159 (1998), pp. 432--491. Linear operator methods in interpolation, moment and extension problems, Semialgebraic sets and related spaces, Moment problems, Hermitian and normal operators (spectral measures, functional calculus, etc.), Subnormal operators, hyponormal operators, etc., Toeplitz operators, Hankel operators, Wiener-Hopf operators, Moment problems and interpolation problems in the complex plane The complex moment problem and subnormality: A polar decomposition approach
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves homotopy groups; algebraic topology of manifolds; fundamental groups; covering spaces; degeneration; monodromy; moduli spaces; elliptic surfaces; curves; surfaces; singularities M. Amram and M. Teicher, On the degeneration, regeneration and braid monodromy of the surface \(T\times T,\) Acta Appl. Math. 75 (2003), 195--270. Fibrations, degenerations in algebraic geometry, Homotopy theory and fundamental groups in algebraic geometry, Fine and coarse moduli spaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Homotopy groups, general; sets of homotopy classes, Euclidean geometries (general) and generalizations On the degeneration, regeneration and braid monodromy of \(T\times T\)
| 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 Taniyama-Weil conjecture; \(L\)-functions; motivic \(L\)-functions; automorphic \(L\)-functions; Fermat's last theorem; arithmetic study of elliptic curves; modular forms A. Knapp, \textit{Elliptic Curves}, Princeton Univ. Press, Princeton, New Jersey (1992). Elliptic curves, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Langlands \(L\)-functions; one variable Dirichlet series and functional equations, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Higher degree equations; Fermat's equation, Elliptic curves over global fields, Rational points 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 survey; research monograph; motives; pure motives; mixed motives; motivic cohomology; algebraic cycles; periods of integrals; Chow groups; K-theory André, Y., Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panor. Synthèses, vol. 17, (2004), Société Mathématique de France Paris Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Period matrices, variation of Hodge structure; degenerations, Transcendence theory of other special functions, Motivic cohomology; motivic homotopy theory, Algebraic cycles An introduction to motives. Pure motives, mixed motives, 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 Calabi-Yau threefolds; fiber product of relatively minimal rational elliptic surfaces with section; automorphisms of rational elliptic surfaces; group actions; non-simply connected Calabi-Yau threefolds; fixed points Automorphisms of surfaces and higher-dimensional varieties, \(3\)-folds, Calabi-Yau manifolds (algebro-geometric aspects), Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces Non-simply connected Calabi-Yau threefolds constructed as quotients of Schoen 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 higher differentials on cyclic curves; basis for cohomology groups Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic ground fields for curves, Cycles and subschemes Higher differentials on cyclic 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 Gröbner bases; syzygies; resolution of singularities; monodromy; Brieskorn lattice; Tate resolution; cohomology of coherent sheaves; Beilinson monads; invariant rings; binary forms; Green's conjecture; construction of canonical curves Schreyer, F.O.: Some topics in computational algebraic geometry. In: Conference Proceedings of 'Advances in Algebra and Geometry, Hyderabad 2001, pp. 263--278 (2003) Computational aspects of algebraic curves, Singularities in algebraic geometry, Computational aspects in algebraic geometry, Syzygies, resolutions, complexes and commutative rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Some topics in computational 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 derived category; exceptional sequence; quasiphantom category; surfaces of general type; surfaces isogenous to a higher product Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Surfaces of general type Exceptional collections on some fake quadrics
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves lower bound for the rank of elliptic curves Elliptic curves, Arithmetic varieties and schemes; Arakelov theory; heights An arithmetical function associated with the rank 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; stable bundles of rank two and degree d; Chern class; De Rham cohomology Gieseker, D., \textit{A degeneration of the moduli space of stable bundles}, J. Differential Geom., 19, 173-206, (1984) Algebraic moduli problems, moduli of vector bundles, de Rham cohomology and algebraic geometry, Formal methods and deformations in algebraic geometry A degeneration of the moduli space of stable bundles
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 curves; degenerations of hypersurfaces; Hilbert scheme; Chern class; Segre class; Chow group Formal methods and deformations in algebraic geometry, Hypersurfaces and algebraic geometry, Curves in algebraic geometry, Parametrization (Chow and Hilbert schemes) On limiting 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 double coverings; nef cone; symmetric product of curves Chan, K.: A characterization of double covers of curves in terms of the ample cone of second symmetric product. J. Pure Appl. Algebra \textbf{212}(12):2623-2632 (2008) Special divisors on curves (gonality, Brill-Noether theory), Coverings of curves, fundamental group A characterization of double covers of curves in terms of the ample cone of second symmetric 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 smash product of Galois algebras; fppf-cohomology Galois theory and commutative ring extensions, Étale and other Grothendieck topologies and (co)homologies Sur le smash-produit des algèbres galoisiennes. (On the smash product of Galois algebras)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 multiplication; elliptic curves; Hecke characters of imaginary quadratic fields Arithmetic ground fields for curves, Complex multiplication and abelian varieties, Quadratic extensions, Elliptic curves, Special algebraic curves and curves of low genus Une classe de courbes elliptiques à multiplication complexe
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 stable curves; rational cohomology ring; natural classes; \(n\)-pointed curves; tautological ring Cornalba, Cohomology of moduli spaces of stable curves, Proceedings of the International Congress of Mathematicians, Doc. Math. Extra Vol. II pp 249-- (1998) Families, moduli of curves (algebraic), Étale and other Grothendieck topologies and (co)homologies, Singularities of curves, local rings Cohomology of moduli spaces of stable 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; Heegner points on elliptic curves; Birch-Stephens conjecture; Tate height of the canonical rational points B. J. Birch and N. M. Stephens, ''Computation of Heegner points,'' in Modular Forms, Chichester: Horwood, 1984, pp. 13-41. Rational points, Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Software, source code, etc. for problems pertaining to algebraic geometry, Special algebraic curves and curves of low genus, Cubic and quartic Diophantine equations Computation of Heegner 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 product of curves; Poincaré-Hodge polynomial; symmetric product of a compact Kähler manifold J. Burillo, ''The Poincaré-Hodge Polynomial of a Symmetric Product of Compact Kähler Manifolds,'' Collect. Math. 41, 59--69 (1990). Transcendental methods, Hodge theory (algebro-geometric aspects), Curves in algebraic geometry, Global differential geometry of Hermitian and Kählerian manifolds, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series The Poincaré-Hodge polynomial of a symmetric product of compact Kähler manifolds
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves families of curves; \(\ell\)-adic cohomology; monodromy representation; degenerations; logarithmic geometry Stix J.: A logarithmic view towards semistable reduction. J. Algebraic Geom. 14(1), 119--136 (2005) Families, moduli of curves (algebraic), \(p\)-adic cohomology, crystalline cohomology, Fibrations, degenerations in algebraic geometry, Structure of families (Picard-Lefschetz, monodromy, etc.), Étale and other Grothendieck topologies and (co)homologies, Infinitesimal methods in algebraic geometry A logarithmic view towards semistable reduction
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Koszul cohomology; rank two vector bundle on curves Vector bundles on curves and their moduli, Syzygies, resolutions, complexes and commutative rings Non-vanishing for Koszul cohomology 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 higher Chow group; motivic cohomology Satoshi Kondo & Seidai Yasuda, ``On two higher Chow groups of schemes over a finite field.'', Doc. Math.20 (2015), p. 737-752 Motivic cohomology; motivic homotopy theory, Homotopy theory and fundamental groups in algebraic geometry, (Equivariant) Chow groups and rings; motives On two higher Chow groups of schemes over a finite 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 elliptic curve cryptosystems; generation of prime order elliptic curves; complex multiplication; class field polynomials Elisavet Konstantinou, Aristides Kontogeorgis, Yannis C. Stamatiou, and Christos Zaroliagis, Generating prime order elliptic curves: difficulties and efficiency considerations, Information security and cryptology --- ICISC 2004, Lecture Notes in Comput. Sci., vol. 3506, Springer, Berlin, 2005, pp. 261 -- 278. Complex multiplication and moduli of abelian varieties, Algebraic number theory computations, Class numbers, class groups, discriminants, Class field theory, Modular and automorphic functions, Cryptography, Applications to coding theory and cryptography of arithmetic geometry Generating prime order elliptic curves: difficulties and efficiency considerations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves irreducible Galois representations; arithmetic of number fields; division points of elliptic curves; projective vectors; complex Galois representations; automorphic representations; \(\ell -adic\) representation Integral representations related to algebraic numbers; Galois module structure of rings of integers, Galois theory, Elliptic curves, Global ground fields in algebraic geometry, Langlands-Weil conjectures, nonabelian class field theory, Representation-theoretic methods; automorphic representations over local and global fields Projective vectors of complex Galois representations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves crystalline cohomology of modular curves; étale cohomology; \(p\)-divisible group; Shimura curve; Fontaine's conjecture Faltings, Gerd, Crystalline cohomology of semistable curve\textemdash the \({\mathbf Q}_p\)-theory, J. Algebraic Geom., 1056-3911, 6, 1, 1\textendash 18 pp., (1997) \(p\)-adic cohomology, crystalline cohomology, Étale and other Grothendieck topologies and (co)homologies, Arithmetic ground fields for curves, Modular and Shimura varieties Crystalline cohomology of semistable curve -- the \(\mathbb{Q}_ p\)-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 representations of knot groups in SO(3) and SU(2); real plane algebraic curves; singularities; Dehn surgery along a two-bridge knot Burde, G., \(S U(2)\)-representation spaces for two-bridge knot groups, Math. Ann., 288, 103-119, (1990) Representations of infinite symmetric groups, Fundamental groups and their automorphisms (group-theoretic aspects), Curves in algebraic geometry \(SU(2)\)-representation spaces for two-bridge knots
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves little discs operads; Hochschild cohomology; algebras of observables; quantum mechanics; deformation quantization; gauge transformations; gauge equivalence class; star products; Poisson manifold; graded Lie superalgebra; Feynman diagrams; Grothendieck-Teichmüller group; operads; algebras over operads; formality theorem; motivic Galois group; higher-dimensional algebras; motives; quantum field theories Maxim Kontsevich, ``Operads and motives in deformation quantization'', Lett. Math. Phys.48 (1999) no. 1, p. 35-72 Deformations of associative rings, Loop spaces, de Rham cohomology and algebraic geometry, Classical real and complex (co)homology in algebraic geometry, Supermanifolds and graded manifolds, Quantum field theory; related classical field theories, Loop space machines and operads in algebraic topology Operads and motives in deformation quantization
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; motivic cohomology J. Park, \textsl{Regulators on additive higher Chow groups}, Amer. J. Math., \textbf{131}, (2009), no. 1, 257--276. DOI 10.1353/ajm.0.0035; zbl 1176.14001; MR2488491; arxiv math/0605702 (Equivariant) Chow groups and rings; motives, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Relations of \(K\)-theory with cohomology theories, Algebraic cycles Regulators on additive higher Chow groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves minimal models; elliptic curves with complex multiplication; Néron model; differential of Weierstraß model Gross, B. H., Minimal models for elliptic curves with complex multiplication, Compos. Math., 45, 155-164, (1982) Minimal model program (Mori theory, extremal rays), Special algebraic curves and curves of low genus, Complex multiplication and abelian varieties, Elliptic curves Minimal models for elliptic curves with complex multiplication
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cyclic isogenies of elliptic curves Arithmetic ground fields for curves, Complex multiplication and abelian varieties, Elliptic curves, Special algebraic curves and curves of low genus A note on orders of isogenies of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Elliptic curve; Tate-Shafarevich group; Selmer group; Pontrjagin dual; formal group; Galois cohomology; cup product; de Rham cohomology; étale cohomology; crystalline cohomology; Néron period; Tate module Kurihara M., ''On the Tate-Shafarevich Groups Over Cyclotomic Fields of an Elliptic Curve with Supersingular Reduction.'' (2000) Elliptic curves over global fields, Iwasawa theory, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over local fields, Étale and other Grothendieck topologies and (co)homologies, de Rham cohomology and algebraic geometry, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Elliptic curves, Formal groups, \(p\)-divisible groups On the Tate-Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction. 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 cohomological Hasse principle; zeta function; Chow group; Bloch map; unramified class field theory, étale cohomology, cycle map, Milnor \(K\)-group; intersection theory; arithmetic geometry; algebraic cycle Research exposition (monographs, survey articles) pertaining to algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Rational points, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives, Local ground fields in algebraic geometry Algebraic cycles and étale cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves supersingular elliptic curves over finite fields; Weierstrass equation; number of rational points F. Morain, Classes d'isomorphismes des courbes elliptiques supersingulières en caracteristique . Util. Math. 52, 241--253 (1997) Elliptic curves over local fields, Curves over finite and local fields, Elliptic curves, Finite ground fields in algebraic geometry Isomorphism classes of supersingular elliptic curves of characteristic \(\geq 3\)
| 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 stable degeneration; isogeny; product of curves D. Mckenzie, On uniformization of compact complex manifolds with negative first Chern class by bounded symmetric domains, Master thesis, Univ. of Cape Town, 2013. Families, moduli, classification: algebraic theory, Deformations of singularities Stable degenerations of surfaces isogenous to a product. 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 third order curves; plane curves; homogeneous functions; projectivity; involution; projective properties of conics; pencil of conics; polar properties; Steiner system; Hesse' curve; pencil of third order curves; Cayley' curve; cubic involution; Steiner's polygon; elliptic functions General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry, Plane and space curves, Elliptic functions and integrals Third order plane curves. A summary of its known properties
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves multilinear algebra; tensor products; algebraic varieties; secant varieties; representation theory; complexity theory; matrices; monograph; textbook; matrix multiplication; tensor decomposition; tensor network; border rank; tensor calculus; projective algebraic geometry; Terracini's Lemma; polynomial Waring problem; Segre varieties; signal processing; Littlewood-Richardson rule; Pieri's formula; Strassen's equation; Young flattening; Friedland's equation; Fano varieties of line; Chow varieties of zero cycle; Brill's equation; normal form; Konstant's theorem; Bott-Borel-Weil theorem; Koszul sequences; syzygies J. M. Landsberg, \textit{Tensors: Geometry and Applications}, American Mathematical Society, Providence, RI, 2012. Vector and tensor algebra, theory of invariants, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra, Multilinear algebra, tensor calculus, Determinantal varieties, Grassmannians, Schubert varieties, flag manifolds, Exterior algebra, Grassmann algebras, Homogeneous spaces and generalizations, Group actions on varieties or schemes (quotients), Representation theory for linear algebraic groups, Characterization and structure theory of statistical distributions, Signal theory (characterization, reconstruction, filtering, etc.), Differential geometric aspects in vector and tensor analysis Tensors: geometry 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 S-algebras; algebraic K-theory of spaces; quantum field theories; elliptic curves; modular forms; even unimodular lattices Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.), Algebraic \(K\)-theory of spaces, Elliptic curves, Elliptic cohomology, Discontinuous groups and automorphic forms Brave new rings
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves vertex operator; parabolic bundle; Verlinde formula; Clebsch-Gordan condition; two dimensional conformal field theory; affine Lie algebra; conformal vacua; highest weight; moduli space of curves Franco, D.: An infinitesimal Torelli for conformal vacua. Comm. Algebra 31, 3795--3810 (2003) Vertex operators; vertex operator algebras and related structures, Vector bundles on curves and their moduli, Relationships between algebraic curves and integrable systems, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics An infinitesimal Torelli for conformal vacua
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Fano manifold; normal projective connection; deformation of a map; scheme; higher direct image sheaf; ample bundle; Chern class; rational curves Ye, Y.-G.: On Fano manifolds with normal projective connections.Int. J. Math. 5 (1994), 265-271. Compact analytic spaces, Moduli, classification: analytic theory; relations with modular forms, Fano varieties, Deformations of complex structures On Fano manifolds with normal projective connections
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 degree equations; elliptic curves Higher degree equations; Fermat's equation, Elliptic curves Rational points of the symmetric diagonal equations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Jacobians; theta-functions; iterated integrals; Epstein zeta function; product of two L-functions; Fermat quartic Theta functions and abelian varieties, Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Iterated integrals and Epstein zeta functions with harmonic rational function coefficients
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Namba's conjecture; hypergeometric series over finite fields; elliptic curves; trace of the Frobenius map Koike, M., Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields, Hiroshima Math. J., 25, 1, 43-52, (1995) Curves over finite and local fields, Other character sums and Gauss sums, Classical hypergeometric functions, \({}_2F_1\), Special functions in characteristic \(p\) (gamma functions, etc.), Finite ground fields in algebraic geometry Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic cohomology; topological modular forms; resolution of the sphere spectrum; chromatic filtration M. Behrens, A modular description of the \(K(2)\)-local sphere at the prime 3, Topology 45 (2006), no. 2, 343--402. Elliptic cohomology, Homotopy groups of spheres, \(v_n\)-periodicity, Primary cohomology operations in algebraic topology, Elliptic curves A modular description of the \(K(2)\)-local sphere at the prime 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 mixed motives; Nisnevich topology; integral motivic cohomology; higher Chow groups; l-adic independency; cdh-topology Cisinski, D. C.; Déglise, F., Integral mixed motives in equal characteristic, (Documenta Mathematica, Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday, (2015)), 145-194 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), (Equivariant) Chow groups and rings; motives, Algebraic cycles, Étale and other Grothendieck topologies and (co)homologies, Motivic cohomology; motivic homotopy theory Integral mixed motives in equal 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 elliptic curves; elliptic schemes; cohomology; Morava E-theory Families, moduli of curves (algebraic), Elliptic cohomology, \(K\)-theory operations and generalized cohomology operations in algebraic topology Modular isogeny complexes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic \(K\)-theory; algebraic cycles; intersection theory; Chow ring; Deligne-Beilinson cohomology; Hodge conjecture; de Rham cohomology; motives Murre, J.P.: Algebraic cycles and algebraic aspects of cohomology and k-theory, In: Albano, A., Bardelli, F. (eds.) Algebraic Cycles and Hodge Theory, Lecture Notes in Mathematics, vol. 1594, pp. 93-152 (1994) Algebraic cycles, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Étale and other Grothendieck topologies and (co)homologies Algebraic cycles and algebraic aspects of cohomology and \(K\)-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 deformation of symmetric product of curves; hyperelliptic curve Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Symmetric products of hyperelliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves canonical height; curves of genus two; rational torsion; Jacobian Stoll, M., On the height constant for curves of genus two, Acta Arith., 90, 2, 183-201, (1999) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Heights, Jacobians, Prym varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\) On the height constant for curves of genus two
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli spaces of stable pointed curves; Weil-Petersson volumes; 1-dimensional cohomological field theories; rational cohomology classes Kaufmann, R.; Manin, Yu.; Zagier, D., Higher {W}eil-{P}etersson volumes of moduli spaces of stable {\(n\)}-pointed curves, Comm. Math. Phys., 181, 3, 763-787, (1996) Families, moduli of curves (algebraic), Singularities of curves, local rings Higher Weil-Petersson volumes of moduli spaces of stable \(n\)-pointed 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 Dirichlet twists of \(L\)-functions; Elliptic curves over number fields Fearnley, J.; Kisilevsky, H.; Kuwata, M., Vanishing and non-vanishing Dirichlet twists of \textit{L}-functions of elliptic curves, J. lond. math. soc. (2), 86, 2, 539-557, (2012) Elliptic curves over global fields, Rational points, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces Vanishing and non-vanishing Dirichlet twists of \(L\)-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 hyper-Kähler manifolds of type \(A_\infty\); Kodaira type; universal cover; fiber space of elliptic curves Special Riemannian manifolds (Einstein, Sasakian, etc.), Elliptic curves On degenerations of elliptic curves and hyper-Kähler 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 differential Horace lemma; prescribed singularities; Picard group; cohomology groups of line bundles; plane curves; geometric genus Mignon, T., Courbes lisses sur les surfaces rationnelles génériques: Un lemme d'Horace différentiel, Ann. Inst. Fourier (Grenoble), 50, 6, 1709-1744, (2000) Rational and ruled surfaces, Plane and space curves, Configurations and arrangements of linear subspaces Smooth curves on generic rational surfaces: a differential Horace lemma
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Brauer group; Prym variety; symmetric product of curves Algebraic cycles, Étale and other Grothendieck topologies and (co)homologies, Brauer groups of schemes, Algebraic moduli problems, moduli of vector bundles, Stacks and moduli problems Brauer groups of schemes associated to symmetric powers of smooth projective curves in arbitrary characteristics
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 forms; moduli stacks of elliptic curves; Cohen-Macaulay Holomorphic modular forms of integral weight, Stacks and moduli problems Additive decompositions for rings of modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher logarithms; Deligne cohomology; Chern classes; functional equation Richard M. Hain, The existence of higher logarithms, Compositio Math. 100 (1996), no. 3, 247 -- 276. \(K\)-theory of schemes, (Co)homology theory in algebraic geometry, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Riemann-Roch theorems, Chern characters The existence of higher logarithms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves textbook; number theory; elliptic curves; arithmetic algebraic geometry; diophantine geometry; computational number theory; cryptography; group cohomology J.H. Silverman, \textit{The arithmetic of elliptic curves}, Graduate Texts in Mathematics \textbf{106}, Springer, Dordrecht, Netherlands (2009). Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Elliptic curves over global fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Elliptic curves over local fields, Abelian varieties of dimension \(> 1\), Curves over finite and local fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves, Rational points, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic ground fields for curves, Number-theoretic algorithms; complexity, Cohomology of groups The arithmetic of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher degree diophantine equations; elliptic curves; modular representations; Taniyama-Weil conjecture Higher degree equations; Fermat's equation, Elliptic curves over global fields, Elliptic curves On the equations \(a^ p+b^ p+15c^ p=0\) and \(a^ p+3b^ p+5c^ p=0\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves number of nonsingular plane elliptic curves; finite ground field Schoof, René, Nonsingular plane cubic curves over finite fields, J. Comb. Theory, Ser. A, 46, 2, 183-211, (1987) Finite ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Elliptic curves Nonsingular plane cubic curves over finite fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves dual curve; characteristic \(p\); strange curves of higher order; osculating planes Kaji, H.,Strangeness of higher order for space curves. Comm. Alg. 20 (1992), 1535--1584. Plane and space curves, Projective techniques in algebraic geometry Strangeness of higher order for space 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 Laurent polynomials; Cayley-Koszul complex; determinant; discriminant of a polynomial in two indeterminates; elliptic curve Gel'fand, I.; Zelevinskiǐand, A.; Kapranov, M., Discriminants of polynomials in several variables and triangulations of Newton polyhedra, Algebra i Analiz, 2, 1, (1990) Toric varieties, Newton polyhedra, Okounkov bodies, Polynomial rings and ideals; rings of integer-valued polynomials, Determinantal varieties Discriminants of polynomials in several variables and triangulations of Newton polyhedra
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 abstract Wiener space; strictly positive selfadjoint operator; exterior product bundle; \(L^ 2\)-sections; \(\overline{\partial}\)- cohomology group; space of harmonic \((p,q)\)-forms; de Rham-Hodge- Kodaira's decomposition T. Nishimura, ''Exterior product bundle over complex abstract Wiener space,''Osaka J. Math.,29, No. 2, 233--245 (1992). Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), de Rham cohomology and algebraic geometry, de Rham theory in global analysis, Measures and integration on abstract linear spaces Exterior product bundle over complex abstract Wiener 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 Tate pairing; discrete logarithm; elliptic curves; multiplicative group of finite fields Frey, G.; Müller, M.; Rüuck, H., The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems, IEEE Transactions on Information Theory, 45, 5, 1717-1719, (1999) Cryptography, Applications to coding theory and cryptography of arithmetic geometry, Number-theoretic algorithms; complexity The Tate pairing and the discrete logarithm applied to 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 moduli space of stable curves; integrable systems; cohomological field theories; double ramification cycle; double ramification hierarchy Rossi, P., Integrability, quantization and moduli spaces of curves, SIGMA, 13, (2017) Families, moduli of curves (algebraic), Relationships between algebraic curves and integrable systems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Integrability, quantization and 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 algebraic cycles; mixed Hodge structures; extensions; regulators; curves; Jacobians; higher Chow cycles; motivic cycles Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Polylogarithms and relations with \(K\)-theory, Transcendental methods, Hodge theory (algebro-geometric aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry The fundamental group and extensions of motives of 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 moduli spaces of curves; curves with level structures; mapping class groups; Torelli group; homology and cohomology of groups; Johnson homomorphism; homological stability A. Putman, The Torelli group and congruence subgroups of the mapping class group, Moduli spaces of Riemann surfaces, IAS/Park City Math. Ser. 20, American Mathematical Society, Providence (2013), 169-196. Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization, Classification theory of Riemann surfaces, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Topological properties of groups of homeomorphisms or diffeomorphisms, Groups acting on specific manifolds The Torelli group and congruence subgroups of the mapping class 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 elliptic surfaces; elliptic curves over function fields; generators of Mordell-Weil group; Kodaira-Néron model; number of minimal sections; specialization homomorphisms Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Elliptic curves, Elliptic curves over global fields, Finite ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations Mordell-Weil lattices and Galois representation. 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 rank of elliptic curves Elliptic curves, Rational points, Elliptic curves over global fields On an estimate of the rank of elliptic curves by multiplication-by-\(m\) map
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves \(L\)-functions of elliptic curves; modularity of elliptic curves; Shimura varieties; motivic Galois modules; mixed Tate motives; Taniyama conjecture; Wiles' famous theorem Arithmetic aspects of modular and Shimura varieties, Research exposition (monographs, survey articles) pertaining to number theory, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Drinfel'd modules; higher-dimensional motives, etc., \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Modular and Shimura varieties Galois modules and Shimura 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 algebraic K-theory; algebraic cycles; Chow group; codimension two cycles; Abel-Jacobi map; norm residue map; higher Picard variety Murre, J.P., Applications of algebraic \textit{K}-theory to the theory of algebraic cycles, (Algebraic geometry, Sitges (Barcelona), 1983, Lecture notes in math., vol. 1124, (1985), Springer Berlin), 216-261 (Equivariant) Chow groups and rings; motives, Parametrization (Chow and Hilbert schemes), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Picard groups Applications of algebraic K-theory to the theory of algebraic cycles
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Gromov-Witten invariants; quantum cohomology; toric varieties; symplectic manifolds; moduli spaces of stable curves; cohomology classes Spielberg, H.: Multiple quantum products in toric varieties, Int. J. Math. math. Sci. 31, No. 11, 675-686 (2002) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Multiple quantum products in toric varieties
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; Cartan modular curves; trace of Hecke operators; cusp forms; Selberg trace formula; non-split dihedral representation; Jacobians; isogeny; explicit formula Chen, Imin, The Jacobians of non-split Cartan modular curves, Proc. London Math. Soc. (3), 77, 1, 1-38, (1998) Arithmetic aspects of modular and Shimura varieties, Spectral theory; trace formulas (e.g., that of Selberg), Jacobians, Prym varieties, Modular and Shimura varieties, Elliptic curves, Hecke-Petersson operators, differential operators (one variable) The Jacobians of non-split Cartan 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 supergroups of automorphisms; supergeometry; supermanifold; elliptic supersymmetric curves; SUSY Levin, A. M., Supersymmetric elliptic curves, Funct. Anal. Appl., 21, 3, 243-244, (1987) Curves in algebraic geometry, Period matrices, variation of Hodge structure; degenerations, Applications of global differential geometry to the sciences, Families, moduli of curves (analytic) Supersymmetric 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 finiteness of Tate-Shafarevich groups of elliptic curves with complex multiplication; elliptic unit; descent Elliptic curves, Elliptic and modular units, Complex multiplication and abelian varieties, Elliptic curves over global fields, Rational points Tate-Shafarevich groups 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 classification up to isomorphism; elementary equivalence; function fields over algebraically closed fields; function fields of curves; elliptic curves D. Pierce , Function fields and elementary equivalence . Bull. London Math. Soc. 31 ( 1999 ), 431 - 440 . MR 1687564 | Zbl 0959.03022 Model-theoretic algebra, Algebraic functions and function fields in algebraic geometry, Elliptic curves, Model theory (number-theoretic aspects), Properties of classes of models Function fields and elementary equivalence
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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 Gromov-Witten invariants; moduli space of curves; quantum cohomology Kimura, T.; Liu, X., A genus-3 topological recursion relation, Comm. Math. Phys., 262, 645, (2006) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Families, moduli of curves (algebraic) A genus-3 topological recursion relation
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; actions of two-groups; complete intersections; complex projective curves Gómez Gutiérrez, V; López de Medrano, S, Surfaces as complete intersections, Contemp. Math., 629, 171-180, (2014) Topology of real algebraic varieties, Complete intersections Surfaces as 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 Beilinson-Deligne cohomology; derived category of weakly admissible filtered modules --------, Syntomic cohomology as a \(p\)-adic absolute Hodge cohomology , to appear in Math. Z. \(p\)-adic cohomology, crystalline cohomology, Local ground fields in algebraic geometry, Relations of \(K\)-theory with cohomology theories Syntomic cohomology as a \(p\)-adic absolute Hodge 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 algebraic cycle homology; codimension 1 cycles; higher Chow groups Friedlander, E. M., \textit{some computations of algebraic cycle homology}, Proceedings of conference on algebraic geometry and ring theory in honor of Michael Artin, Part III (Antwerp, 1992), Vol. 8, 271-285, (1994) (Co)homology theory in algebraic geometry, Algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Some computations of algebraic cycle homology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; elliptic functions; Riemann surfaces of genus one Edwards, H.M.: A normal form for elliptic curves. Bulletin of the American Mathematical Society~44, 393--422 (2007), http://www.ams.org/bull/2007-44-03/S0273-0979-07-01153-6/home.html (Cited in {\S}2.2) Elliptic curves, Elliptic functions and integrals A normal form for 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 Mordell-Weil groups of elliptic curves with complex; multiplication; Weil parametrizations; L-function attached to a Weil curve; anti-cyclotomic tower; Iwasawa theory of elliptic curves; p-adic height pairing; p-adic L-functions; p-adic Heegner measures; finiteness of the Tate-Shafarevich group; Mordell-Weil groups of elliptic curves with complex multiplication B. Mazur, Modular curves and arithmetic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 185 -- 211. Arithmetic ground fields for curves, Complex multiplication and abelian varieties, Theta series; Weil representation; theta correspondences, Elliptic curves, Global ground fields in algebraic geometry, Local ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Complex multiplication and moduli of abelian varieties Modular curves and arithmetic
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves explicit computations of Chow rings; regular quadratic forms; product formula; quadrics Shapiro, D.B.; Szyjewski, M., Product formulas for quadratic forms, Bol. soc. mat. mexicana, 37, 463-474, (1992) Quadratic forms over general fields, Sums of squares and representations by other particular quadratic forms, Algebraic cycles Product formulas for 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 factoring integers; cryptography; elliptic curve computations over fields of characteristic two; ElGamal cryptosystem A.J. Menezes, S. Vanstone, The implementation of elliptic curve cryptosystems, in: Advances in cryptology --- AUSCRYPT '90, Lecture Notes in Computer Science, vol. 453, Springer, Berlin, 1990, pp. 2 -- 13. Cryptography, Elliptic curves The implementation of 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 number of points of intersection of two space curves; hypersurface containing two space curves Diaz, S.: Space curves that intersect often, Pac. J. Math. 123, No. 2, 263-267 (1986) Special algebraic curves and curves of low genus, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Low codimension problems in algebraic geometry, Enumerative problems (combinatorial problems) in algebraic geometry Space curves that intersect often
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves period conjecture of Gross-Deligne; complex multiplication; arithmetic fixed point formula; equivariant analytic torsion; Hodge conjecture; de Rham cohomology; Betti structure Maillot, V; Rössler, D, On the periods of motives with complex multiplication and a conjecture of Gross-Deligne, Ann. Math., 160, 727-754, (2004) Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties, Complex multiplication and abelian varieties On the periods of motives with complex multiplication and a conjecture of Gross-Deligne
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 parametrizations of elliptic curves; Manin constant; isogeny class; minimal Parshin-Faltings height; Stickelberger elements; Antwerp tables Stevens, G.: Stickelberger elements and modular parametrizations of elliptic curves. Invent. Math. 98(1), 75--106 (1989) Special algebraic curves and curves of low genus, Global ground fields in algebraic geometry, Holomorphic modular forms of integral weight, Elliptic curves Stickelberger elements and modular parametrizations of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic normal curves; irregular surfaces in \(\mathbb{P}^4\); Hartshorne-Rao modules; Heisenberg modules; Moore matrices; syzygies of bielliptic surfaces; abelian surfaces; liaison; elliptic scrolls Alf Aure, Wolfram Decker, Klaus Hulek, Sorin Popescu, and Kristian Ranestad, Syzygies of abelian and bielliptic surfaces in \?\(^{4}\), Internat. J. Math. 8 (1997), no. 7, 849 -- 919. Special surfaces, Syzygies, resolutions, complexes and commutative rings, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves Syzygies of abelian and bielliptic surfaces in \(\mathbb{P}^4\). -- Appendix by C. Ciliberto and K. Hulek
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves irreducible characters; finite groups of Lie type; connected reductive group; Frobenius map; maximal torus; Borel subgroup; Deligne-Lusztig virtual characters; \(\ell \)-adic cohomology; semisimple classes; Jordan decomposition; irreducible constituents Linear algebraic groups over finite fields, Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Simple groups: alternating groups and groups of Lie type, Ordinary representations and characters, Group actions on varieties or schemes (quotients) Détermination des caractères des groupes finis simples: Travaux de Lusztig. (Determination of characters of finite simple groups: Work of Lusztig)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Gauge theory with finite gauge group; cobordism; topological quantum field theory; Picard groupoid of Hermitian lines; cohomology with coefficeints in Picard groupoid; gerbe; cap product Topological field theories in quantum mechanics, Topological quantum field theories (aspects of differential topology), Groupoids, semigroupoids, semigroups, groups (viewed as categories), Groupoids (i.e. small categories in which all morphisms are isomorphisms), Picard groups Categorification of Dijkgraaf-Witten 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 Kronecker's Jugendtraum; elliptic functions; elliptic integrals; arithmetic of elliptic curves; Weierstrass \(\wp\)-function; projective plane cubics; Abel's theorem; inversion problem; Jacobi functions; theta functions; Lefschetz theorem; embeddings; theta identities; Euler identities; Jacobi substitutions; quadratic reciprocity; Siegel modular group; modular forms; Eisenstein series; modular equation; arithmetic subgroups; arithmetic applications; solvability of algebraic equations; Galois theory; Klein's icosaeder; quintic equation; imaginary quadratic number fields; class invariants; class polynomial; Mordell-Weil theorem Henry McKean and Victor Moll, \textit{Elliptic Curves}, Cambridge University Press, Cambridge, 1997. Research exposition (monographs, survey articles) pertaining to number theory, Elliptic curves over global fields, Elliptic curves, Elliptic functions and integrals, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Quadratic extensions, Class numbers, class groups, discriminants, Equations in general fields, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Structure of modular groups and generalizations; arithmetic groups, Research exposition (monographs, survey articles) pertaining to algebraic geometry Elliptic curves. Function theory, geometry, arithmetic
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves spinor variety; orthogonal Grassmannian; elliptic curve; quantum cohomology; Chow group Homogeneous spaces and generalizations, Grassmannians, Schubert varieties, flag manifolds, Special algebraic curves and curves of low genus, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Elliptic curves on spinor 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 torsion points of elliptic curves; ramification; Kummer generators Elliptic curves, Rational points Ramification of the Kummer extension generated from torsion points 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 weight distributions of families of codes; families of elliptic curves over finite fields; numbers of rational points on the curves Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Curves over finite and local fields Codes 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 codimension-two subscheme; cohomology of complete intersection; smooth deformation Sauer, T.: Codimension-two subvarieties of ? n with the cohomology of a complete intersection. Math. Z.188, 143-148 (1985) Low codimension problems in algebraic geometry, Complete intersections, Classical real and complex (co)homology in algebraic geometry, Formal methods and deformations in algebraic geometry Codimension-two subvarieties of \({\mathbb{P}}^ n\) with cohomology of a complete intersection
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves flag variety; number of double contacts; families of plane curves; Chow groups; triple contacts Enumerative problems (combinatorial problems) in algebraic geometry, Parametrization (Chow and Hilbert schemes), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Proof of Schubert's conjectures on double contacts
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 height function; Fermat Last Theorem; finiteness conjectures in Diophantine geometry; degenerate set of integral points; analogy between the theory of Diophantine approximation in number theory and value distribution theory; Nevanlinna theory; local height function; abc- conjecture; size of integral points on elliptic curves P. Vojta, Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987. Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Research exposition (monographs, survey articles) pertaining to number theory, Value distribution theory in higher dimensions, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic ground fields for curves, Global ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties Diophantine approximations and value distribution 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 elliptic curves over global fields; arithmetic surfaces; zeta function; zeta integral; two-dimensional adelic spaces; harmonic analysis; Hasse zeta functions; analytic duality; boundary term; meromorphic continuation and functional equation; mean-periodic functions; Laplace; Carleman transform; generalized Riemann hypothesis; Birch and Swinnerton; Dyer conjecture; automorphic representations Fesenko, I.: Adelic approach to the zeta function of arithmetic schemes in dimension two. Moscow Math. J. \textbf{8}(2), 273-317 (2008) (http://www.maths.nottingham.ac.uk/personal/ibf/ada.pdf) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Generalized class field theory (\(K\)-theoretic aspects) Adelic approach to the zeta function of arithmetic schemes in dimension 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 coherent functor; noetherian ring; discrete valuation ring; coherent sheaf; cohomology of sheaves; duality; liaison; Rao functor; space curves; linkage Hartshorne, R., \textit{coherent functors}, Adv. Math., 140, 44-94, (1998) Homological methods in commutative ring theory, Local categories and functors, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Linkage, Plane and space curves Coherent functors
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves arithmetically C-M space curve; numerical character; maximal rank curves in the linkage class of two skew lines Bolondi, G.: On the classification of curves linked to two skew lines. Texte zur Mathematik, no. 92, 38-52 (1986) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Families, moduli of curves (algebraic) On the classification of curves linked to two skew lines
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 forms; topological modular forms; tmf; moduli stack of elliptic curves Elliptic cohomology, Stable homotopy theory, spectra, Moduli, classification: analytic theory; relations with modular forms, Holomorphic modular forms of integral weight, Stacks and moduli problems Rings of modular forms and a splitting of \(\mathrm{TMF}_0(7)\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; double ramification cycle; universal Jacobian Families, moduli of curves (algebraic), Jacobians, Prym varieties Compactified universal Jacobian and the double ramification cycle
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Chern class; Hodge bundle; moduli spaces of principally polarized abelian varieties; moduli space of curves with a level two structure; theta characteristic; Weierstrass points Hain, R; Reed, D, Geometric proofs of some results of Morita, J. Algebraic Geom., 10, 199-217, (2001) Families, moduli of curves (algebraic), Jacobians, Prym varieties, Fine and coarse moduli spaces, Classical real and complex (co)homology in algebraic geometry, Algebraic moduli of abelian varieties, classification, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (analytic) Geometric proofs of some results of Morita
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; linear varieties; Künneth spectral sequences; motivic cohomology; Künneth formula R Joshua, Algebraic \(K\)-theory and higher Chow groups of linear varieties, Math. Proc. Cambridge Philos. Soc. 130 (2001) 37 \(K\)-theory of schemes, (Equivariant) Chow groups and rings; motives, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Motivic cohomology; motivic homotopy theory Algebraic \(K\)-theory and higher Chow groups of linear varieties
| 0 |
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