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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic integer; radix expression; window nonadjacent expansion; algorithm; point multiplication of elliptic curves; cryptography Blake, Ian F.; Murty, V. Kumar; Xu, Guangwu, Nonadjacent radix-\textit{ {\(\tau\)}} expansions of integers in Euclidean imaginary quadratic number fields, Canad. J. Math., 60, 6, 1267-1282, (2008) Algebraic numbers; rings of algebraic integers, Radix representation; digital problems, Number-theoretic algorithms; complexity, Algebraic number theory computations, Applications to coding theory and cryptography of arithmetic geometry Nonadjacent radix-\(\tau\) expansions of integers in Euclidean imaginary quadratic number fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve; rank of the Mordell-Weil group; twists; Galois cohomology Elliptic curves over global fields, Rational points, Elliptic curves Ranks 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 cup product; de Rham cohomology; Mumford curves; Stokes theorem de Rham cohomology and algebraic geometry, Arithmetic ground fields for curves, Local ground fields in algebraic geometry, Congruences for modular and \(p\)-adic modular forms, Differentials on Riemann surfaces, Topological properties in algebraic geometry A formula for the cup product on Mumford curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves intersection of two curves Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Enumerative problems (combinatorial problems) in algebraic geometry On the reduction of the class of a product curve by the presence of a point of inflection
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves public-key cryptography; elliptic curves; co-\(Z\) coordinates; out-of-place formulæ; Montgomery ladder; embedded systems Cryptography, Applications to coding theory and cryptography of arithmetic geometry Memory-constrained implementations of elliptic curve cryptography in co-\(Z\) coordinate repre\-sentation
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves arithmetic geometry codes; curves with many rational points; modular curves; class field theory; Deligne-Lusztig curves; infinite global fields; decoding of AG-codes; sphere packings; codes from multidimensional varieties; quantum AG-codes Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to information and communication theory, Curves in algebraic geometry, Theory of error-correcting codes and error-detecting codes, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic numbers; rings of algebraic integers, Algebraic coding theory; cryptography (number-theoretic aspects), Zeta and \(L\)-functions in characteristic \(p\), Class field theory, Zeta functions and \(L\)-functions of number fields, Fine and coarse moduli spaces, Arithmetic ground fields for surfaces or higher-dimensional varieties Algebraic geometry codes: advanced chapters
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves with complex multiplication; elliptic curves over an imaginary quadratic field; Iwasawa theory; supersingular primes; Schneider-Greenberg conjecture; \(p^ m\)-torsion subgroups; \(\mathbb{Z}_ p\)-cyclotomic extensions; maximal proextensions; special values of modular \(L\)-functions; elliptic units Mcconnell, G.: On the Iwasawa theory of CM elliptic curves at supersingular primes, Compos. math. 101, 1-19 (1996) Iwasawa theory, Elliptic curves over global fields, Elliptic curves, Complex multiplication and moduli of abelian varieties On the Iwasawa theory of CM elliptic curves at supersingular primes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves indecomposable division algebras; noncrossed product division algebras; patching over fields; smooth projective curves; completions of function fields; Brauer groups Chen, F.: Indecomposable and noncrossed product division algebras over curves over complete discrete valuation rings, (2010) Finite-dimensional division rings, Brauer groups (algebraic aspects), Brauer groups of schemes, Algebraic functions and function fields in algebraic geometry Indecomposable and noncrossed product division algebras over curves over complete discrete valuation 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 rank two stable reflexive sheaf; bound for the third Chern class; bound on genus of curves in projective 3-space Hartshorne, R, Stable reflexive sheaves III, Math. Ann., 279, 517-534, (1988) Curves in algebraic geometry, Characteristic classes and numbers in differential topology Stable reflexive sheaves. III
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves fundamental group of irreducible curve; representation for curves of higher genus; Galois action; monodromy action Coverings of curves, fundamental group, Galois theory, Group actions on varieties or schemes (quotients) Galois action on the nilpotent completion of the fundamental group of an algebraic curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves characteristic \(p\); Galois group of number fields of curves; elliptic curve; potentially good reduction Kraus, A., Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive, Manuscripta Math., 69, 1, 353-385, (1990) Arithmetic ground fields for curves, Local ground fields in algebraic geometry, Galois theory On the failure of semistability of elliptic curves with additive 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 mixed motives; \(K\)-groups; elliptic curves; Deligne period; entropy C. Deninger, On extensions of mixed motives. Preprint 1995. Generalizations (algebraic spaces, stacks), \(K\)-theory of schemes, Drinfel'd modules; higher-dimensional motives, etc. On extensions of mixed motives
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of marked Riemann surfaces; singular Riemann surfaces; Lie algebras of meromorphic vector fields; elliptic curves; complex tori; algebraic geometric degeneration; Riemann sphere M. Schlichenmaier, ''Degenerations of Generalized Krichever-Novikov Algebras on Tori,'' J. Math. Phys. 34, 3809--3824 (1993). Virasoro and related algebras, Riemann surfaces; Weierstrass points; gap sequences Degenerations of generalized Krichever-Novikov algebras on tori
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves generalized Riemann hypothesis; family of elliptic curves; even analytic rank; odd analytic rank Families, moduli of curves (algebraic), Elliptic curves, Elliptic curves over global fields The average analytic rank of a family 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 Lubin-Tate Curves; Deligne-Lusztig varieties; local Langlands; etale cohomology; unramified representations Representation theory for linear algebraic groups, Linear algebraic groups over finite fields, Étale and other Grothendieck topologies and (co)homologies, Curves over finite and local fields, Representation-theoretic methods; automorphic representations over local and global fields Cuspidal representations in the cohomology of Deligne-Lusztig varieties for \(\mathrm{GL}(2)\) over finite 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 algebraic cycle; elliptic variety; standard conjecture of Lefschetz type; \(K3\) surface; abelian scheme Tankeev, S G, On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models, Izv. Ross. Akad. Nauk Ser. Mat., 78, 181-214, (2014) Algebraic cycles, Variation of Hodge structures (algebro-geometric aspects), Classical real and complex (co)homology in algebraic geometry, \(4\)-folds On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; cohomology ring; partial differential equation Relationships between algebraic curves and physics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Families, moduli of curves (algebraic) The bi-Hamiltonian structures of the DR and DZ hierarchies in the approximation up to genus one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic genera; elliptic cohomology theory; coefficients; rings of modular forms; complex bordism; formal groups; addition formula for elliptic integrals of the first kind; integrality; divisibility; universal elliptic genus Landweber, P.S.: Elliptic Cohomology and Modular Forms. In: Landweber, P.S. (ed.) Elliptic Curves and Modular Forms in Topology. Proceedings. Princeton 1986. (Lect. Notes Math., vol. 1326, pp. 55--68), Berlin Heidelberg New York: Springer 1988 Characteristic classes and numbers in differential topology, Holomorphic modular forms of integral weight, Other homology theories in algebraic topology, Riemann-Roch theorems, Families, moduli of curves (analytic) Elliptic cohomology and modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Bloch filtration; pure motives; Hodge conjecture; category of mixed motives; category of geometric mixed Hodge structures; category of mixed Hodge structure of geometric origin; absolute Hodge cohomology; Deligne cohomology; mixed Hodge modules of geometric origin Saito, M., \textit{Hodge conjecture and mixed motives. I}, Complex geometry and Lie theory (Sundance, UT, 1989), 283-303, (1991), American Mathematics Society, Providence, RI Transcendental methods, Hodge theory (algebro-geometric aspects), Generalizations (algebraic spaces, stacks), Variation of Hodge structures (algebro-geometric aspects) Hodge conjecture and mixed motives. 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 Hilbert theorem 90 for K2; norm residue homomorphism; roots of unity; K- cohomology groups of Severi-Brauer varieties; \(K_ 2\) of division algebras; second Chow group; cohomology classes with zero restriction A. S. Merkur'ev and A. A. Suslin, ''The norm residue homomorphism,'' Preprint LOMI, P-6-82, Leningrad (1982). Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(K\)-theory of global fields, Étale and other Grothendieck topologies and (co)homologies, Grothendieck groups, \(K\)-theory, etc., (Equivariant) Chow groups and rings; motives Norm residue homomorphism
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; tautological ring; double ramification cycle Janda, F.; Pandharipande, R.; Pixton, A.; Zvonkine, D., Double ramification cycles on the moduli spaces of curves, Publ. Math. Inst. Hautes Études Sci., 125, 221-266, (2017) Families, moduli of curves (algebraic), Algebraic cycles Double ramification cycles on the moduli spaces of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Krichever-Novikov algebras; universal central extension; untwisted affine Kac-Moody algebra; Kassel's theorem; Kähler differentials; hyperelliptic curves; elliptic curve with punctures at two points; cocycles; Pollaczek polynomials M. R. Bremner, ''Universal central extensions of elliptic affine Lie algebras'',J. Math. Phys. 35, 6685--6692 (1994). Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Elliptic curves, Differentials on Riemann surfaces Universal central extensions of elliptic affine Lie 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 filtration of a module; finitely generated module; cycle class; Chow group; Grothendieck group; Riemann-Roch map Chan, C.-Y.: Filtrations of modules, the Chow group, and the Grothendieck group. J. Algebra \textbf{219}(1), 330-344 (1999) Grothendieck groups, \(K\)-theory and commutative rings, (Equivariant) Chow groups and rings; motives, \(K_0\) of other rings Filtrations of modules, the Chow group, and the Grothendieck 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 curve; obstruction group for realizing characters; Brauer group; Galois cohomology; unramified Brauer group; reciprocity law; hyperelliptic curves Brauer groups of schemes, Elliptic curves Brauer groups of curves and reciprocity laws in Brauer groups of their function fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves one-parameter families of elliptic K3 surfaces; parabolic cohomology; Hodge structure; Torelli mapping \(K3\) surfaces and Enriques surfaces, Transcendental methods, Hodge theory (algebro-geometric aspects), Elliptic curves Notes on elliptic K3 surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves injective homomorphism of product of local rings; length formulas for the local cohomology; module of differential forms on a complete intersection with isolated singularity Bruns, W. andVetter, U., Length formulas for the local cohomology of exterior powers,Math. Z. 191, (1986), 145--158. Homological dimension and commutative rings, Dimension theory, depth, related commutative rings (catenary, etc.), Local cohomology and algebraic geometry, Complete intersections Length formulas for the local cohomology of exterior powers
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Diophantine tuples; elliptic curves; elliptic surfaces; \(K3\) surfaces; higher moments; bias conjecture Elliptic curves, \(K3\) surfaces and Enriques surfaces, Quadratic and bilinear Diophantine equations, Elliptic curves over global fields Diophantine triples and \(K3\) surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves relative cohomology; Deligne cohomology; sheaves of differentials; Weil algebra; gerbes; characteristic classes Bloch, S. and Esnault, H., Relative algebraic differential characters, (None) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Families, moduli of curves (algebraic), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Vector bundles on curves and their moduli, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Relative algebraic differential characters
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves over finite fields; rational points on elliptic curves; rank of elliptic curves Thus the optimum is attained for P = Y X(X>X)-1 and V = (X>X)-1 X>Y X(X>X)-1. 33 Elliptic curves over global fields, Elliptic curves over local fields, Curves over finite and local fields, Elliptic curves The elliptic curves \(y^2=x(x-1)(x-\lambda )\).
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomology of Severi-Brauer varieties; Gersten spectral sequence; Riemann-Roch formula for higher \(K\)-groups; \(K_2\); Milnor functor; norm residue homomorphism; Brauer group; Hilbert theorem 90 for \(K_2\) A. S. Merkurcprimeev and A. A. Suslin, ''\(K\)-cohomology of Severi-Brauer varieties and the norm residue homomorphism,'' Izv. Akad. Nauk SSSR Ser. Mat., vol. 46, iss. 5, pp. 1011-1046, 1135, 1982. \(K_2\) and the Brauer group, Higher symbols, Milnor \(K\)-theory, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Galois cohomology, (Equivariant) Chow groups and rings; motives, \(K\)-theory of global fields, Galois cohomology, \(K\)-theory of local fields, Brauer groups of schemes, Galois cohomology \(K\)-cohomology of Severi-Brauer varieties and the norm residue homomorphism
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves high rank curves; infinite family of elliptic curves with rank 11 Tetsuji Shioda, An infinite family of elliptic curves over \? with large rank via Néron's method, Invent. Math. 106 (1991), no. 1, 109 -- 119. Elliptic curves, Elliptic curves over global fields An infinite family of elliptic curves over \(\mathbb{Q}\) with large rank via Néron's method
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; mapping class groups; elliptic curves Benjamin Collas, ''Action of a Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups of genus one'', Int. J. Number Theory 8 (2012) no. 3, p. 763-787 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus Action of a Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups of genus one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic cycles; higher Chow groups; mixed Tate motives; admissible cycle; polylogarithms; minimal models Bloch, S.: Algebraic cycles and the Lie algebra of mixed Tate motives,J. Amer. Math. Soc. 4 (1991), 771--791. Generalizations (algebraic spaces, stacks), Algebraic cycles, Minimal model program (Mori theory, extremal rays), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry Algebraic cycles and the Lie algebra of mixed Tate motives
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Bertini theorem; curves of arithmetic genus 2; cuspidal elliptic curve; cuspidal rational curve Fibrations, degenerations in algebraic geometry, Rational and birational maps, Families, moduli of curves (algebraic), Singularities of curves, local rings, Elliptic curves Fibrations by non-smooth projective curves of arithmetic genus two in characteristic two
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Birch-Swinnerton-Dyer conjecture; Mordell-Weil rank of elliptic curves Brumer, Armand; McGuinness, Oisín., The behavior of the Mordell-Weil group of elliptic curves, Bull. Amer. Math. Soc. (N.S.), 23, 2, 375-382, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) The behavior of the Mordell-Weil group 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 Birch--Swinnerton-Dyer conjecture; rank; group of rational points; elliptic curves; class number; quadratic fields \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Elliptic curves, Rational points On the rank and the BSD conjecture of elliptic curves \(E_D\colon y^2=x^3-D^3\)
| 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 tautological ring; Faber conjectures; moduli of curves; Gromov-Witten theory; cohomology of moduli spaces Petersen, D., Tautological rings of spaces of pointed genus two curves of compact type, Compos. math., 152, 1398-1420, (2016) Families, moduli of curves (algebraic), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects), Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Variation of Hodge structures (algebro-geometric aspects), Fiberings with singularities in algebraic topology Tautological rings of spaces of pointed genus two curves of compact type
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cuspidal plane curves; higher homology groups; number of singularities Zaĭdenberg, M. G.; Orevkov, S. Yu.: On rigid rational cuspidal plane curves, Uspekhi mat. Nauk 51, No. 1(307), 149-150 (1996) Singularities of curves, local rings, Special algebraic curves and curves of low genus, Classical real and complex (co)homology in algebraic geometry On rigid rational cuspidal plane 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 rings of differential operators and their modules; local cohomology; characteristic variety; characteristic cycle; critical cone Commutative rings of differential operators and their modules, Local cohomology and algebraic geometry On invariants of modules over the ring of differential operators
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 stack of elliptic curves; vector bundles 10.1016/j.jalgebra.2015.01.007 Families, moduli of curves (algebraic), Elliptic curves, Algebraic moduli problems, moduli of vector bundles, Stacks and moduli problems Vector bundles on the moduli stack 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 curves; \(p\)-torsion points; field of definition Lozano-Robledo, Á., On the field of definition of p-torsion points on elliptic curves over the rationals, Math. Ann., 357, 279-305, (2013) Elliptic curves, Elliptic curves over global fields, Global ground fields in algebraic geometry On the field of definition of \(p\)-torsion points on elliptic curves over the rationals
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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 Hecke quantum unique ergodicity rate conjecture; Hannay-Berry model of quantum mechanics on the two-dimensional torus; arithmetic quantum chaos; canonical model; Deligne's letter; geometric Weil representation; Weil representation Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity, Vanishing theorems in algebraic geometry, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Noncommutative geometry (à la Connes), Quantum chaos Proof of the Kurlberg-Rudnick rate conjecture
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Models of curves; tame cyclic quotient singularities,; group actions on cohomology; Néron models Halle, L. H.: Galois actions on Néron models of Jacobians, Ann. inst. Fourier 60, No. 3, 853-903 (2010) Fibrations, degenerations in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Positive characteristic ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Picard schemes, higher Jacobians Galois actions on Néron models of Jacobians
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; Iwasawa theory; \(p\)-adic heights; \(p\)-adic \(L\)-function; height pairing of abelian varieties; Iwasawa function; rational point of infinite order; Tate duality Karl Rubin, Abelian varieties, \?-adic heights and derivatives, Algebra and number theory (Essen, 1992) de Gruyter, Berlin, 1994, pp. 247 -- 266. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights Abelian varieties, \(p\)-adic heights and derivatives
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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 neural network of final ring; secret sharing schemes; system of residual classes; elliptic curves Elliptic curves, Finite fields (field-theoretic aspects) Elliptic threshold secret division scheme
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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 algorithm for subsystems of a root system; simple elliptic singularities; singular del Pezzo surfaces; Coxeter diagram; intersections of two quadrics; deformations of singularities C.\ T.\ C. Wall, Root systems, subsystems and singularities, J. Alg. Geom. 1 (1992), 597-638. Singularities in algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Computational aspects of algebraic surfaces, Deformations of complex singularities; vanishing cycles Root systems, subsystems and singularities
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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 non-abelian cohomology; moduli space of curves Hain, Rational points of universal curves, J. Amer. Math. Soc. 24 pp 709-- (2011) Rational points, Other nonalgebraically closed ground fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) Rational points of universal 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 Lang-Trotter conjecture; Sato-Tate conjecture; parametric families of elliptic curves Sha, M.; Shparlinski, IE, Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves, Acta Arith., 170, 299-325, (2015) Farey sequences; the sequences \(1^k, 2^k, \dots\), Elliptic curves over global fields, Curves over finite and local fields, Elliptic curves Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Deligne-Beilinson cohomology; mixed elliptic motives Hain, R.: Deligne-Beilinson cohomology of affine groups. [arXiv:1507.03144] [math.AG] Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Transcendental methods, Hodge theory (algebro-geometric aspects), Variation of Hodge structures (algebro-geometric aspects), Period matrices, variation of Hodge structure; degenerations, Transcendental methods of algebraic geometry (complex-analytic aspects), Group schemes Deligne-Beilinson cohomology of affine groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of pointed curves of genus 0; Weil-Petersson volumes; Künneth formula for quantum cohomology; Calabi-Yau manifolds Families, moduli of curves (algebraic), (Co)homology theory in algebraic geometry, Generalized (extraordinary) homology and cohomology theories in algebraic topology, String and superstring theories; other extended objects (e.g., branes) in quantum field theory The geometry of moduli spaces of pointed curves, the tensor product in the theory of Frobenius manifolds and the explicit Künneth formula in quantum 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 \(K3\) surfaces; Chow ring; Beauville-Voisin's zero-cycle; deformation of morphisms; singularities. \(K3\) surfaces and Enriques surfaces Singularities of elliptic curves in \(K3\) surfaces and the Beauville-Voisin zero-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 genus three curves; Jacobian; twist; Klein quartic; Dyck-Fermat quartic; non-abelian Galois cohomology Stephen Meagher & Jaap Top, Twists of genus three curves over finite fields, Finite Fields Appl.16 (2010), p. 347-368 Curves over finite and local fields, Rational points, Finite ground fields in algebraic geometry Twists of genus three curves over finite fields
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves rational cohomology groups of moduli space of stable \(n\)-pointed genus \(g\) curves Arbarello, E.; Cornalba, M., Calculating cohomology groups of moduli spaces of curves via algebraic geometry, Publ. Math. Inst. Hautes Études Sci., 88, 97-127, (1998) Families, moduli of curves (algebraic), Étale and other Grothendieck topologies and (co)homologies, Algebraic moduli problems, moduli of vector bundles Calculating cohomology groups of moduli spaces of curves via 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 torsion points of elliptic curves; diagonalizable group scheme M. Yasuda, M. Torsion points of elliptic curves with good reduction, Kodai Math. J. 31 (2008), no. 3, 385--403. Group schemes, Elliptic curves over global fields, Elliptic curves Torsion points of elliptic curves with good reduction
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves motivic Steenrod algebra; cohomology of motivic Steenrod algebra; Massey product; periodicity Massey products, Steenrod algebra, Adams spectral sequences, Motivic cohomology; motivic homotopy theory The \(v_1\)-periodic region in the cohomology of the \(\mathbb{C}\)-motivic Steenrod algebra
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves construction of elliptic curves from automorphic Hecke newforms; Drinfeld modular curves; Shimura-Taniyama-Weil conjecture; Jacobian; strong Weil curve; strong Weil uniformization Gekeler, E-U; Reversat, M, Jacobians of Drinfeld modular curves, J. für die reine und angewandte Mathematik, 476, 27-93, (1996) Drinfel'd modules; higher-dimensional motives, etc., Modular and Shimura varieties, Jacobians, Prym varieties, Elliptic curves over global fields Jacobians of Drinfeld modular 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 elliptic curves; generators; group of rational points; Mordell-Weil lattice invariant H. E. Rose, On a class of elliptic curves with rank at most two, Math. Comp. 64 (1995), no. 211, 1251 -- 1265, S27 -- S34. Elliptic curves over global fields, Elliptic curves, Cubic and quartic Diophantine equations, Software, source code, etc. for problems pertaining to number theory, Computational aspects of algebraic curves On a class of elliptic curves with rank at most two
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomology ring; graded Frobenius algebras; cup product; cohomology of Hilbert scheme Lehn, M; Sorger, C, The cup product of Hilbert schemes for \(K3\) surfaces, Invent. Math., 152, 305-329, (2003) Parametrization (Chow and Hilbert schemes), Minimal model program (Mori theory, extremal rays), \(K3\) surfaces and Enriques surfaces, Products and intersections in homology and cohomology The cup product of Hilbert schemes for K3 surfaces
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves coverings of elliptic curves with complex multiplication; hyperelliptic curves; character sums; normalizing conditions Leprévost, F.; Morain, F., Revêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères, J. Number Theory, 64, 165-182, (1997) Complex multiplication and moduli of abelian varieties, Elliptic curves over global fields, Elliptic curves, Other character sums and Gauss sums Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves torsion of elliptic curves Arithmetic ground fields for curves, Elliptic curves, Special algebraic curves and curves of low genus On exact estimates for torsion of curves of genus one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cyclotomic unit; arithmetic of an elliptic curve; Mordell-Weil group; Tate-Shafarevich group; Birch and Swinnerton-Dyer conjecture; Weil curves; Selmer group; family of Heegner points; elliptic units V. A. KOLYVAGIN, The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 52, no. 6 (1988), pp. 1154-1180, 1327; translation in Math. USSR-Izv., 33, no. 3 (1989), pp. 473-499. Zbl0681.14016 MR984214 Arithmetic ground fields for curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special algebraic curves and curves of low genus, Global ground fields in algebraic geometry, Elliptic curves On the Mordell-Weil and Shafarevich-Tate groups for elliptic Weil curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves function fields; algebraic varieties; divisors; line bundles; vector bundles; sheaves; cohomology; elliptic curves; curves over arithmetic fields; Belyi's theorem; algebraic curves; one-dimensional varieties; coherent sheaves on curves; Riemann-Roch theorem; hyperelliptic curves; Serre duality Algebraic functions and function fields in algebraic geometry, Vector bundles on curves and their moduli, Valuations and their generalizations for commutative rings, Elliptic curves, Riemann-Roch theorems, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra, Arithmetic ground fields for curves Algebraic curves and one-dimensional 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 cubic surface; moduli space; curves of genus three; odd theta- characteristic Families, moduli of curves (algebraic), Theta functions and abelian varieties, Rational and unirational varieties, Algebraic moduli of abelian varieties, classification The moduli space of curves of genus three together with an odd theta- characteristic is rational
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves symmetric product; algebraic cycle; Chow group Polishchuk, Selecta Math. 13 pp 531-- (2007) (Equivariant) Chow groups and rings; motives, Algebraic cycles, Jacobians, Prym varieties Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. I
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves De Rham cohomology; crystalline action of Weil group; Morita's \(p\)-adic gamma function; absolute Hodge cycles; Frobenius matrix of Fermat curves Ogus, A, A \(p\)-adic analogue of the chowla-Selberg formula, \(p\)-adic analysis (Trento, 1989), Lect. Notes Math., 1454, 319-341, (1990) Local ground fields in algebraic geometry, Arithmetic ground fields for curves, de Rham cohomology and algebraic geometry A \(p\)-adic analogue of the Chowla-Selberg formula
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Fundamental group; varieties isogenous to a product of curves; quotient varieties; quotient group. Dedieu, T.; Perroni, F.: The fundamental group of a quotient of a product of curves. J. group theory 15, No. 3, 439-453 (2012) Homotopy theory and fundamental groups in algebraic geometry, Surfaces of general type The fundamental group of a quotient of a product of curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve over a global function field; Mordell-Weil lattices; determinants; cycle-class map; crystalline cohomology; height pairing [3] N. Dummigan, `` The determinants of certain Mordell-Weil lattices {'', \(Amer. J. Math.\)117 (1995), no. 6, p. 1409-1429. &MR 13 | &Zbl 0914.} Elliptic curves over global fields, Lattices and convex bodies (number-theoretic aspects), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, \(p\)-adic cohomology, crystalline cohomology The determinants of certain Mordell-Weil lattices
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; twists of elliptic curves; Selmer groups; graph; Neumann-Setzer type elliptic curves Elliptic curves over global fields, Elliptic curves, Zeta functions and \(L\)-functions of number fields, Applications of graph theory to circuits and networks Partitions of graphs and Selmer groups of elliptic curves of Neumann-Setzer type
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Cremona transformations; birational transformation of three-dimensional projective space; Chow ring; blowing up Birational automorphisms, Cremona group and generalizations, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Certain numerical relations for three-dimensional Cremona transformations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves filtration on the Chow group; Abel-Jacobi map; regulator; Deligne cohomology; Hodge structure; Jannsen conjecture; Bloch-Beilinson conjecture Lewis, J.: A filtration on the Chow groups of a complex projective variety. Compos. Math. 128(3), 299--322 (2001) Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), (Equivariant) Chow groups and rings; motives A filtration on the Chow groups of a complex projective variety
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves torsion subgroup of Galois group; Iwasawa theory; elliptic curves; imaginary quadratic field; \({bbfZ}_{\ell }\)-extension; abelian extension; maximal abelian p-extension Cyclotomic extensions, Elliptic curves, Iwasawa theory, Galois theory Nombres de classes dans certaines extensions infinies. (Class numbers in some infinite extensions)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves generation of elliptic curves; complex multiplication; class polynomials Applications to coding theory and cryptography of arithmetic geometry, Cryptography, Elliptic curves, Complex multiplication and moduli of abelian varieties, Class numbers, class groups, discriminants, Algebraic coding theory; cryptography (number-theoretic aspects) Ramanujan's class invariants and their use in elliptic curve cryptography
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli of curves; graph complexes; cohomology Families, moduli of curves (algebraic), Geometric aspects of tropical varieties Tropical curves, graph complexes, and top weight cohomology of \(\mathcal{M}_g\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 analog of the Bloch-Suslin complex; modular elliptic curves A. B. Goncharov and A. M. Levin, Zagier's conjecture on \(L(E,2)\), Invent. Math. 132 (1998), 393--432. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Zagier's conjecture on \(L(E,2)\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves exterior Galois representations; fundamental groups of punctured elliptic curves; Grothendieck's anabelian conjecture Cadoret, A., Tamagawa, A.: On subgroups of \({GL}_r(\mathbb{F}_l)\) and representations of étale fundamental groups. Preprint. http://www.math.polytechnique.fr/~cadoret/Travaux.html Elliptic curves over global fields, Coverings of curves, fundamental group, Galois representations, Elliptic and modular units On exterior Galois representations associated with open 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 intersections of three quadrics; varieties of planes; cohomology Rationality questions in algebraic geometry, Complete intersections Varieties of planes on intersections of three 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 Hilbert scheme; almost complex structure; pseudoholomorphic curves; desingularization; symmetric product; Hilbert-Chow morphism Voisin C.: On the Hilbert scheme of points of an almost complex fourfold. Ann. Inst. Fourier (Grenoble) 50(2), 689--722 (2000) Parametrization (Chow and Hilbert schemes), General geometric structures on manifolds (almost complex, almost product structures, etc.) On the Hilbert scheme of points of an almost complex fourfold
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves computational aspects of elliptic curves; modular parametrization; strong Weil curve Cremona, [Cremona 97] J. E., \textit{Algorithms for Modular Elliptic Curves}, (1997), Cambridge University Press, Cambridge Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Number-theoretic algorithms; complexity, Analytic computations, Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory Algorithms for modular elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves family of elliptic curves; positive Mordell-Weil rank Ono, T.: Triangles and elliptic curves. I -- VI. Proc. Japan Acad., 70A, 106-108(1994): 70A, 223-225 (1994) ; 70A, 311-314 (1994); 71A, 104-106 (1995); 71A, 137-139 (1995); 71A, 184-186. Elliptic curves, Elliptic curves over global fields, Cubic and quartic Diophantine equations Triangles 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 moduli space of Riemann surfaces; Deligne-Mumford compactification; spectral sequence; mixed Hodge structure; stable cohomology; tautological class; \( \operatorname{BV} \)-algebra; Maurer-Cartan equation; quantum master equation Vanishing theorems in algebraic geometry, Families, moduli of curves (analytic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) On the \(\operatorname{BV}\) structure on the cohomology of moduli space
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves complex algebraic curves; Teichmüller theory; elliptic curves; modular forms; Picard groups; hyperbolic geometry; classification of compact Riemann surfaces; moduli theory of compact Riemann surfaces Richard Hain, Moduli of Riemann surfaces, transcendental aspects, School on Algebraic Geometry (Trieste, 1999) ICTP Lect. Notes, vol. 1, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000, pp. 293 -- 353. Families, moduli of curves (algebraic), Classification theory of Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Moduli of Riemann surfaces, transcendental aspects
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves torsion points; computation of modular elliptic curves; modular symbols; non-torsion points; heights; isogenies; periods; rank J. Cremona, Algorithms for modular elliptic curves. Cambridge: Cambridge University Press, 1992. Zbl0758.14042 MR1201151 Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Number-theoretic algorithms; complexity, Analytic computations, Symbolic computation and algebraic computation, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory Algorithms for modular elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves curves of genus 5; semistable vector bundle; Clifford index; Brill-Noether theory; higher rank Brill-Noether theory Lange, H.; Newstead, P. E., Higher rank BN-theory for curves of genus \(5\), Rev. Mat. Complut., 29, 691-717, (2016) Vector bundles on curves and their moduli Higher rank BN-theory for curves of genus 5
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves zeta function; Shimura variety; product of L-functions; cohomology of arithmetic groups C. Soule : Cohomologie des groupes discrets et formes automorphes , in Variétés de Shimura et Fonctions L, par L. Breen, J-P. Labesse , Publ. Math. de l'Univ. Paris VII, Paris (1979) p. 131-143. 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, Representation-theoretic methods; automorphic representations over local and global fields Cohomologie des groupes discrets et formes automorphes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function Masser, D. W.; Wüstholz, G., Fields of large transcendence degree generated by values of elliptic functions, Invent. Math., 72, 3, 407-464, (1983) Transcendence theory of elliptic and abelian functions, Varieties over global fields, Global ground fields in algebraic geometry Fields of large transcendence degree generated by values of elliptic functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic cycles; Chow ring; motives; Bloch-Beilinson filtration; hyperkähler variety; Lagrangian subvariety; constant cycle subvariety; (Hilbert scheme of) \(K3\) surface; Beauville's splitting property; multiplicative Chow-Künneth decomposition; spread of algebraic cycles (Equivariant) Chow groups and rings; motives, Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects) Lagrangian subvarieties in the Chow ring of some hyperkähler 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 Chow group; codimension-two cycles of the moduli space C. F. Faber, Some results on the codimension-two Chow group of the moduli space of stable curves , Algebraic curves and projective geometry (Trento, 1988), Lecture Notes in Math., vol. 1389, Springer, Berlin, 1989, pp. 66-75. Parametrization (Chow and Hilbert schemes), Families, moduli of curves (algebraic) Some results on the codimension-two Chow group of the moduli space 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 class field theory for curves over local fields; abelian fundamental group; class field theory of two-dimensional local fields; reciprocity law Saito S.: Class field theory for curves over local fields. J. Number Theory 21(1), 44--80 (1985) Geometric class field theory, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Class field theory; \(p\)-adic formal groups, Local ground fields in algebraic geometry, Coverings in algebraic geometry, Homotopy theory and fundamental groups in algebraic geometry, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) Class field theory for curves over local 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 Getzler's cohomological relation; moduli space of 4 pointed elliptic curves; elliptic Gromov-Witten invariants; Virasoro conjecture Pandharipande, R., A geometric construction of Getzler's elliptic relation. Math. Ann., 313 (1999), 715--729. Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Families, moduli of curves (algebraic) A geometric construction of Getzler's elliptic 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 \(n\)-contact curve; elliptic curves; representation of divisors; Zariski tuple Topological properties in algebraic geometry, Plane and space curves, Elliptic curves, Computational aspects of algebraic curves An explicit construction for \(n\)-contact curves to a smooth cubic via divisions of polynomials and Zariski tuples
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Massey products; Deligne cohomology; Čech resolutions; differential forms; elliptic curve; Beilinson conjectures C. Deninger, ''Higher order operations in Deligne cohomology,''Invent. Math.,122, No. 1, 289--316 (1995). Massey products, (Co)homology theory in algebraic geometry, Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture Higher order operations in Deligne cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves two-dimensional topological quantum field theory; quantum cohomology; symplectic manifolds; algebraic curves; moduli spaces Y. Ruan and G. Tian, ''A mathematical theory of quantum cohomology,'' Math. Res. Lett., vol. 1, iss. 2, pp. 269-278, 1994. Moduli problems for differential geometric structures, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Families, moduli of curves (analytic), Manifolds of mappings, Enumerative problems (combinatorial problems) in algebraic geometry, Topological field theories in quantum mechanics, Topological properties in algebraic geometry, Families, moduli of curves (algebraic), Topological quantum field theories (aspects of differential topology) A mathematical theory of quantum cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; tautological ring; cohomology ring Petersen, D, The structure of the tautological ring in genus one, Duke Math J, 163, 777-793, (2014) Families, moduli of curves (algebraic), Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) The structure of the tautological ring in genus one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves intersection number of two divisors; normal surface; bivariant intersection theory; Chow group; rational equivalence; algebraic equivalence S. Kimura, Fractional intersection and bivariant theory, Comm. Algebra 20 (1992), no. 1, 285-302. (Equivariant) Chow groups and rings; motives, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Algebraic cycles Fractional intersection and bivariant 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 finite fields; distribution of group orders Elliptic curves over global fields, Curves over finite and local fields, Global ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry On group orders of rational 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 curve with seminatural cohomology; smoothable curves; problem of maximal genus; Horace's method; Hilbert scheme of space curves Plane and space curves, Formal methods and deformations in algebraic geometry, Projective techniques in algebraic geometry, Classical real and complex (co)homology in algebraic geometry, Vanishing theorems in algebraic geometry Space curves with the expected postulation
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 Special algebraic curves and curves of low genus, Arithmetic ground fields for curves, Elliptic curves, Rational points Differents of points of torsion
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Deligne periods; Beilinson periods; Tate twist of cohomology of smooth projective variety; cohomological realisations; L-function \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Generalizations (algebraic spaces, stacks) Deligne's conjecture
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves decomposition of uniform fiber bundles over Grassmannian; cohomology ring of flag variety; Chow ring Guyot, M, Caractérisation par l'uniformité des fibrés universels sur la grassmanni-enne, Math. Ann., 270, 47-62, (1985) Sheaves in algebraic geometry, Cycles and subschemes, Grassmannians, Schubert varieties, flag manifolds Caractérisation par l'uniformité des fibrés universels sur la grassmannienne
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Quillen K-groups; Chow groups; zeta function of varieties over finite field; étale cohomology groups; crystalline cohomology groups; Tate's conjecture James Stuart Milne, ``Values of zeta functions of varieties over finite fields'', Am. J. Math.108 (1986) no. 2, p. 297-360 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), (Equivariant) Chow groups and rings; motives, \(p\)-adic cohomology, crystalline cohomology, Arithmetic problems in algebraic geometry; Diophantine geometry, Finite ground fields in algebraic geometry Values of zeta functions of varieties over finite fields
| 0 |
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