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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 Riemann surfaces; holomorphic functions; algebraic curves; de Rham cohomology; elliptic functions; elliptic integrals; uniformization; Jacobians; moduli spaces; deformations Donaldson, S., Riemann Surfaces, Oxford Graduate Texts in Mathematics, vol. 22, (2011), Oxford University Press: Oxford University Press Oxford Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable, Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (analytic), Jacobians, Prym varieties, Conformal mappings of special domains Riemann surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves duality theorem of Galois cohomology groups related to abelian varieties; higher dimensional local fields; Weil-Barsotti formula; higher Tate duality Yoshihiro Koya. On a duality theorem of abelian varieties over higher dimensional local fields. {\em Kodai Math. J.}, 2:297--308, 2000 Local ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Class field theory; \(p\)-adic formal groups On a duality theorem for abelian varieties over higher dimensional 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 zeta-functions of binary Hermitian forms; representations of numbers; genus; Dirichlet series; local densities; Hilbert symbol; Eisenstein series; tables; special values of Eisenstein series; representation numbers; Fourier coefficients of cusp forms of weight 2; L-series of certain elliptic curves; periods Jürgen Elstrodt, Fritz Grunewald, and Jens Mennicke, Zeta-functions of binary Hermitian forms and special values of Eisenstein series on three-dimensional hyperbolic space, Math. Ann. 277 (1987), no. 4, 655 -- 708. Analytic theory (Epstein zeta functions; relations with automorphic forms and functions), Theta series; Weil representation; theta correspondences, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Hurwitz and Lerch zeta functions, Modular and automorphic functions, Waring's problem and variants, General binary quadratic forms, Special algebraic curves and curves of low genus Zeta-functions of binary Hermitian forms and special values of Eisenstein series
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves computational number theory; elliptic curve method; probabilistic algorithm; factorization method; multiplicative groups of elliptic curves over finite fields; running time; comparison Lenstra, H. W., Factoring integers with elliptic curves, \textit{Annals of Mathematics}, 126, 3, 649-673, (1987) Primes, Software, source code, etc. for problems pertaining to number theory, Elliptic curves, Finite ground fields in algebraic geometry, Analysis of algorithms and problem complexity Factoring integers with 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 order of the Tate-Shafarevich group; conductor; discriminant; modular elliptic curves; Birch-Swinnerton-Dyer conjecture Goldfeld, D; Szpiro, L, Bounds for the order of the Tate-Shafarevich group, Compositio Math., 97, 71-87, (1995) \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves Bounds for the order of the Tate-Shafarevich 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 Selmer groups; quadratic twists of elliptic curves Elliptic curves over global fields, Rational points Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion 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 central division algebras over the function field of a curve; Brauer group; elliptic curves V. I. Yanchevskiĭ and G. L. Margolin, Brauer groups of local hyperelliptic curves with good reduction, Algebra i Analiz 7 (1995), no. 6, 227 -- 249 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 7 (1996), no. 6, 1033 -- 1048. V. I. Yanchevskiĭ and G. L. Margolin, Erratum: ''Brauer groups of local hyperelliptic curves with good reduction'', Algebra i Analiz 8 (1996), no. 1, 237 (Russian). Brauer groups of schemes, Elliptic curves, Quaternion and other division algebras: arithmetic, zeta functions The Brauer groups of local hyperelliptic curves with good 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 stable curves; determinant of cohomology line bundle; section ring; conformal blocks Vector bundles on curves and their moduli, Algebraic moduli problems, moduli of vector bundles, Geometric invariant theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics On finite generation of the section ring of the determinant of cohomology line bundle
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; torsion group; modular surface; elliptic Elliptic curves over global fields, Global ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations The rank of elliptic curves with nontrivial torsion 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 rational solutions of cubic Diophantine equations; complex multiplication; elliptic curves; group of endomorphisms; rational points Wajngurt, C.: Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication. J. number theory 23, 80-85 (1986) Special algebraic curves and curves of low genus, Complex multiplication and abelian varieties, Cubic and quartic Diophantine equations, Rational points, Algebraic functions and function fields in algebraic geometry, Elliptic curves Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to 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 rank; families of elliptic curves; complex multiplications Mestre J.-F., C. R. Acad. Sci. Paris Sésr. I Math. 327 (8) pp 763-- (1998) Elliptic curves over global fields, Elliptic curves On the rank of some families of elliptic curves of given invariant
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves rationality questions; rational points; Hasse-Weil \(L\)-function of modular elliptic curves; local-global principles; Selmer's curve; smooth projective varieties; Tate-Shafarevich group; Tate-Shafarevich conjecture; Selmer groups of elliptic curves; class field theory; Kolyvagin test classes Mazur B.: On the passage from local to global in number theory. Bull. Amer. Math. Soc. (N.S.) 29(1), 14--50 (1993) Global ground fields in algebraic geometry, Local ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic ground fields for surfaces or higher-dimensional varieties, Arithmetic ground fields for abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) On the passage from local to global in number theory
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves characteristic 3; group of rational points; elliptic curve; Tate- Shafarevich product; principal homogeneous spaces Elliptic curves, Local ground fields in algebraic geometry, Rational points, Elliptic curves over local fields Tate-Shafarevich products in elliptic curves over pseudolocal fields with residue fields of characteristic 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 cohomology of sheaves; Chow groups; morphism of an algebraic surface; Gysin map; adele representation; differentials; tame symbol English transl. in D. V. Osipov 1997 \textit{Sb. Math.}188 5 697--723 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, \(K\)-theory of local fields, Adèle rings and groups, Local cohomology and algebraic geometry, Symbols, presentations and stability of \(K_2\), Homology and cohomology theories in algebraic topology, Valued fields Adele constructions of direct images of differentials and symbols
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 on 3-folds; Fano variety of index two; twistor curve; minimal twistor spaces; Fano variety; Fano threefolds DOI: 10.1093/qmath/45.3.343 \(3\)-folds, Twistor theory, double fibrations (complex-analytic aspects), Fano varieties Twistor spaces and Fano 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 real Gromov-Witten invariants recursion; enumeration of real curves; WDVV-type relation; Deligne-Mumford moduli P. Georgieva and A. Zinger, Enumeration of real curves in \begin{document}\(\mathbb{C}\mathbb{P}^{2n-1}\)\end{document} and a WDVV relation for real Gromov-Witten invariants, arXiv: 1309.4079. Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Enumeration of real curves in \(\mathbb{CP}^{2n-1}\) and a Witten-Dijkgraaf-Verlinde-Verlinde relation for real Gromov-Witten invariants
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; elliptic curve cryptosystems; metric; isomorphism classes of elliptic curves Mishra, P. K.; Gupta, K. C., A metric on the set of elliptic curves over \(\mathbb{F}_p\), \textit{Applied Mathematics Letters}, 21, 12, 1330-1332, (2008) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry A metric on the set of elliptic curves over \(\mathbb{F}_p\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves p-adic analog of the Weierstrass sigma function; complex elliptic curves; formal group; canonical heights; characteristic p; p-adic theta functions Fontaine, J.-M.: Le corps des périodes \(p\)-adiques. With an appendix by Pierre Colmez. Périodes \(p\)-adiques (Bures-sur-Yvette, 1988). Astérisque No. 223, pp. 59-111 (1994) Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Theta functions and abelian varieties The \(p\)-adic sigma function
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves foliations; André-Oort conjecture; Pila-Wilkie theorem; Weierstrass polydiscs; simultaneous torsion points on square of elliptic curves; Galois orbit; torsion point on elliptic curves; special points on Shimura varieties Rational points, Heights, Model theory of ordered structures; o-minimality, Modular and Shimura varieties Point counting for foliations over 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 moduli of prinipal bundles; binomial ideals; fiber product; weighted graph; Deligne-Mumford stack; Verlinde formula; Gröbner basis; Koszul algebra Manon, C., Coordinate rings for the moduli stack of \(\mathbf{sl}_2(\mathbb{C})\) quasi-parabolic principal bundles on a curve and toric fiber products, J. Algebra, 365, 163-183, (2012) Algebraic moduli problems, moduli of vector bundles, Vector bundles on curves and their moduli Coordinate rings for the moduli stack of \(\mathrm{SL}(\mathbb C)\) quasi-parabolic principal bundles on a curve and toric fiber products
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves faithfulness of the monodromy representation; elliptic curve; Galois representation; algebraic fundamental groups; genus; family of \(n\)-pointed algebraic curves M. Asada, The faithfulness of the monodromy representations associated with certain families of algebraic curves, J. Pure Appl. Algebra 159 (2001), no. 2-3, 123-147. Families, moduli of curves (algebraic), Homotopy theory and fundamental groups in algebraic geometry, Coverings of curves, fundamental group, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) The faithfulness of the monodromy representations associated with certain families of algebraic 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; twisted elliptic curves; discriminant of a quadratic field \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Arithmetic ground fields for curves, Rational points, Elliptic curves, Global ground fields in algebraic geometry, Special algebraic curves and curves of low genus A finiteness criterion for the number of rational points for twisted 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 commuting pair of linear ordinary differential operators; vector bundle; classifications of the smooth elliptic curves; automorphism group; algebra of differential operators; indecomposable and decomposable bundles E. Previato and G. Wilson, \textit{Differential operators and rank }2 \textit{bundles over elliptic} \textit{curves}. Compositio Math. 81 (1992), no. 1, 107--119. General theory of ordinary differential operators, Vector bundles on curves and their moduli, Elliptic curves, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Differential operators and rank 2 bundles over 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 Chow ring; étale cohomology; crystalline cohomology; universal cycle classes; local complete intersections; intersection theory on singular varieties Henri Gillet, Universal cycle classes, Compositio Math. 49 (1983), no. 1, 3 -- 49. Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(p\)-adic cohomology, crystalline cohomology, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies Universal cycle classes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; scalar multiplication; two-dimensional decompositions B. Smith, Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians, in \textit{Algorithmic arithmetic, geometry, and coding theory, contemporary mathematics}, vol. 637 (Amer. Math. Soc., Providence, RI, 2015), pp. 127-141. Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Number-theoretic algorithms; complexity, Applications to coding theory and cryptography of arithmetic geometry Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cycles of codimension 2; motivic cohomology; finiteness of second Chow group; vanishing of cohomology group Salberger, P.: Torsion cycles of codimension 2 and \ell-adic realizations of motivic cohomology. Séminaire de théorie des nombres 1991--92, 247-277 (1993) Parametrization (Chow and Hilbert schemes), Algebraic cycles, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Divisors, linear systems, invertible sheaves Torsion cycles of codimension 2 and \(\ell\)-adic realizations of motivic cohomology
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves circular units; Jacobian of Fermat curves; Galois representations; pro-\(\ell\) braid groups; étale covering of projective 1-space; representation in outer automorphism group of profinite fundamental; group; absolute Galois group; completed group algebra; Tate module; Jacobi sums; Galois cohomology Y. Ihara: Profinite braid groups, Galois representations and complex multiplications. Ann. of Math., 123, 43-106 (1986). JSTOR: Galois theory, Jacobians, Prym varieties, Complex multiplication and abelian varieties, Special algebraic curves and curves of low genus, Coverings of curves, fundamental group, Global ground fields in algebraic geometry, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Galois cohomology Profinite braid groups, Galois representations and complex multiplications
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Heegner points; \(L\)-functions; singular moduli of elliptic curves; discriminants of imaginary quadratic fields Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic ground fields for curves Singular moduli at the Heegener points for general discriminants
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves regulator; polylogarithm; zeta function; Hopf algebra; rational homotopy theory; cohomology of groups; Deligne cohomology; de Rham cohomology; Lie algebra cohomology Burgos Gil, J.I.: The Regulators of Beilinson and Borel. CRM Monographs, vol.~15. American Math. Soc., Providence (2002) Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Research exposition (monographs, survey articles) pertaining to \(K\)-theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry The regulators of Beilinson and Borel
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves automorphism group of curve; product of projective curves; Betti numbers; diagonal quotient surface; desingularizations; Chern numbers; Enriques-Kodaira classification Kani E., Schanz W. (1997). Diagonal quotient surfaces. Manuscripta Math. 93(1):67--108 Homogeneous spaces and generalizations, Families, moduli, classification: algebraic theory, Singularities of surfaces or higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations, Curves in algebraic geometry Diagonal quotient surfaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; hyper-elliptic curves; Jacobians; arithmetic-geometric mean; theta functions; elliptic integrals; algorithm of Richelot Bost, Jean-Benoît.; Mestre, Jean-François, Moyenne arithmético-géométrique et périodes des courbes de genre \(1\) et \(2\), Gaz. Math., 38, 36-64, (1988) Analytic theory of abelian varieties; abelian integrals and differentials, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, History of algebraic geometry, Elliptic curves, History of mathematics in the 19th century Arithmetic-geometric mean and periods of curves of genus 1 and 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 modular function \(j(\tau)\); singular moduli; prime factorization of the absolute norm; modular polynomial; arithmetic of maximal orders in quaternion algebras; geometry of supersingular elliptic curves; Fourier coefficients; Eisenstein series; Hilbert modular group; local heights; Heegner points Gross, B. H.; Zagier, D. B., \textit{on singular moduli}, J. Reine Angew. Math., 355, 191-220, (1985) Modular and automorphic functions, Algebraic moduli of abelian varieties, classification, Special algebraic curves and curves of low genus, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Quaternion and other division algebras: arithmetic, zeta functions On singular moduli
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves weighted projective lines; nilpotent operators; invariant subspace problem; triangle singularities; tilting objects; ADE-chains; Calabi-Yau fractional categories; stable categories of vector bundles; vector bundles on smooth elliptic curves Kussin, D.; Lenzing, H.; Meltzer, H., Nilpotent operators and weighted projective lines, J. Reine Angew. Math., 685, 33-71, (2013) Representations of associative Artinian rings, Module categories in associative algebras, Derived categories and associative algebras, Representations of quivers and partially ordered sets, Singularities in algebraic geometry, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Representation type (finite, tame, wild, etc.) of associative algebras Nilpotent operators and weighted projective 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 analytic description of algebraic endomorphisms; extensions of elliptic curves by tori; transcendence; numbers related to Weierstrass sigma function; complex multiplication; algebraic groups; theta function BERTRAND (D.) et LAURENT (M.) . - Propriétés de transcendance de nombres liés aux fonctions thêta , C. r. Acad. Sci. Paris, Ser. A, t. 292, 1981 , p. 747-749. MR 82k:10037 | Zbl 0472.10033 Transcendence (general theory), Elliptic curves, Complex multiplication and abelian varieties Propriétés de transcendance de nombres liés aux fonctions thêta
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves normal surface singularities; rational singularities; elliptic singularities; \( \mathbb{Q} \)-homology spheres; geometric genus; link of singularities; divisorial filtration; Poincaré series; Seiberg-Witten invariants of 3-manifolds; Casson invariant conjecture; Seiberg-Witten invariant conjecture; Heegaard-Floer homology; graded roots; surgery 3-manifolds; unicuspidal rational projective plane curves Singularities in algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Complex surface and hypersurface singularities, Applications of global analysis to structures on manifolds, Modifications; resolution of singularities (complex-analytic aspects) Pairs of invariants of surface singularities
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic plane curve; holomorphic self-maps; obstructions; invariants at singular points; ordinary singularities; backward orbit; invariant critical components; Julia set; invariant smooth cubics; elementary maps; dual of smooth cubic; Fermat cubic; tangent process; symmetries; Weierstrass' \(\sigma\) and \(\zeta\) functions; elliptic quartics with two singular points; Cassini quartic; quartics with a cusp and a node; mixed quartic; invariant cuspidal quartic [BD02]A. Bonifant and M. Dabija, \textit{Self-maps of }P 2\textit{with invariant elliptic curves}, in: Complex Manifolds and Hyperbolic Geometry (Guanajuato, 2001), Contemp. Math. 311, Amer. Math. Soc., Providence, RI, 2002, 1--25. Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Projective techniques in algebraic geometry, Elliptic curves Self-maps of \(\mathbb{P}^2\) with invariant elliptic curves
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of curves; Chow ring Izadi, E.: The Chow ring of the moduli space of curves of genus 5. In: The Moduli Space of Curves (Texel Island, 1994). Progr. Math., vol. 129, pp. 267--304. Birkhaüser Boston, Boston, MA (1995) Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes) The Chow ring of the moduli space of curves of genus 5
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves congruences; algebraic equations; permutations; permutation groups; elliptic curves; higher-order equations Equations in general fields, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Research exposition (monographs, survey articles) pertaining to field theory, Theta functions and curves; Schottky problem, Curves in algebraic geometry Treatise on permutations and algebraic equations.
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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 with complex multiplication; elliptic units; cohomology class Elliptic and modular units, Complex multiplication and moduli of abelian varieties, Units and factorization, Complex multiplication and abelian varieties On units related to the arithmetic 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 Weierstrass family of elliptic curves; lifted p-adic homology G. C. Kato, Lifted \( p\)-adic homology with compact supports of Weierstrass family and zeta matrices (in preparation). Elliptic curves, Families, moduli of curves (algebraic), \(p\)-adic cohomology, crystalline cohomology Lifted p-adic homology with compact supports of the Weierstrass family and its zeta endomorphism
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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 Braid groups; Yang-Baxter groups; dynamical Yang-Baxter relations; classical Yang-Baxter relations; Kohno-Drinfeld algebras; 3-term relations algebras; Gaudin elements; Jucys-Murphy elements; small quantum cohomology; \(K\)-theory of flag varieties; Pieri rules; chromatic number; Tutte and Betti polynomials; reduced polynomials; Chan-Robbins-Yuen polytope; \(k\)-dissections of a convex \((n+k+1)\)-gon; Lagrange inversion formula; Richardson permutations; multiparameter deformations of Fuss-Catalan and Schröder polynomials; poly-Bernoulli numbers; Stirling numbers; Euler numbers; Brauer algebras; VSASM; CSTCPP; Birman-Ko-Lee monoid; Kronecker elliptic sigma functions Kirillov, Anatol N., On some quadratic algebras {I}~{\(\frac{1}{2}\)}: combinatorics of {D}unkl and {G}audin elements, {S}chubert, {G}rothendieck, {F}uss--{C}atalan, universal {T}utte and reduced polynomials, SIGMA. Symmetry, Integrability and Geometry. Methods and Applications, 12, 002, 172~pages, (2016) Classical problems, Schubert calculus, Yang-Baxter equations, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials
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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 factorization of polynomials; elliptic curves; local-global principle; cubic surfaces Research exposition (monographs, survey articles) pertaining to number theory, Elliptic curves over global fields, Elliptic curves over local fields, Polynomials in number theory, Special surfaces, Computational number theory Computer-aided serendipity
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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 codimension \(r\) algebraic cycles; Griffiths group; Chow group; cycle class map; Galois cohomology; null-homologous cycles Schoen, C, On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field, Ann. Sci.éc. Norm. Supér., 28, 1-50, (1995) Algebraic cycles, Parametrization (Chow and Hilbert schemes), Finite ground fields in algebraic geometry On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraicity of values of the gamma function; de Rham cohomology groups; etale cohomology groups; absolute Hodge cycle; abelian varieties of CM- type Deligne, P., \textit{Hodge cycles on abelian varieties}, Hodge cycles, motives, and Shimura varieties, (1982), Springer, Berlin-New York Transcendental methods, Hodge theory (algebro-geometric aspects), de Rham cohomology and algebraic geometry, Analytic theory of abelian varieties; abelian integrals and differentials, Gamma, beta and polygamma functions Hodge cycles on abelian varieties. (Notes by J. S. Milne)
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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 monster group; modular polynomial; coefficients; \(j\)-invariants of supersingular elliptic curves Modular and automorphic functions, Fourier coefficients of automorphic forms, Algebraic functions and function fields in algebraic geometry On Ito's observation on coefficients of the modular polynomial
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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 Krichever map; Weierstrass cycle; moduli space of curves; tautological ring J.-M. Liou and A. Schwarz, \textit{Weierstrass cycles in moduli spaces and the Krichever map}. arXiv:1207.0530v3 [math.AG], 2014. Families, moduli of curves (algebraic) Weierstrass cycles in moduli spaces and the Krichever map
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Grothendieck ring of varieties; motivic measure; \(\ell\)-adic Galois representations; weight filtration; zeta function; non-isogenous elliptic curves Naumann N.: Algebraic independence in the Grothendieck ring of varieties. Trans. Am. Math. Soc. 359(4), 1653--1683 (2007) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Varieties and morphisms, Motivic cohomology; motivic homotopy theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Varieties over finite and local fields Algebraic independence in the Grothendieck ring of varieties
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves modular curve; abelian varieties with twist; \(X_ 0\); simple factors of the Jacobian variety; correspondence between cusp forms of weight 2 and elliptic curves; Taniyama-Weil conjecture J.E. Cremona, Abelian varieties with extra twist, cusp forms, and elliptic curves over imaginary quadratic fields, J. London Math. Soc. (2), 45 (1992), 404-416. MR 93h:11056 Arithmetic ground fields for abelian varieties, Modular and Shimura varieties, Abelian varieties of dimension \(> 1\), Elliptic curves over global fields, Holomorphic modular forms of integral weight, Quadratic extensions Abelian varieties with extra twist, cusp forms, and elliptic curves over imaginary quadratic 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 quantum cohomology; Gromov-Witten invariants; symmetric products of algebraic curves; Brill-Noether theory Bertram, A.; Thaddeus, M., On the quantum cohomology of a symmetric product of an algebraic curve, Duke Math. J., 108, 329-362, (2001) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Special divisors on curves (gonality, Brill-Noether theory) On the quantum cohomology of a symmetric product of an algebraic curve.
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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 smooth generic fiber; Calabi-Yau threefolds; positive characteristics; Hodge spectral sequence; fibrations; product of an elliptic curve and a rational curve; Hodge duality Hirokado M. (2001). Calabi-Yau threefolds obtained as fiber products of elliptic and quasi-elliptic rational surfaces. J. Pure Appl. Algebra 162: 251--271 Calabi-Yau manifolds (algebro-geometric aspects), \(3\)-folds, Rigid analytic geometry, Transcendental methods, Hodge theory (algebro-geometric aspects) Calabi-Yau threefolds obtained as fiber products of elliptic and quasi-elliptic rational 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 intersection theory; tropical variety; intersection product; Psi-class; moduli of curves Kerber, M; Markwig, H, Intersecting psi-classes on tropical \(M_{0, n}\), Int. Math. Res. Not., 2009, 221-240, (2009) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Enumerative problems (combinatorial problems) in algebraic geometry, Polyhedra and polytopes; regular figures, division of spaces Intersecting Psi-classes on tropical \(\mathcal M_{0,n}\)
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic cycle; Chow group; singular scheme; formal scheme; Tate algebra; rigid geometry; motivic cohomology; Milnor \(K\)-theory; algebraic de Rham cohomology; de Rham-Witt form Algebraic cycles, Higher symbols, Milnor \(K\)-theory, Formal power series rings, Formal neighborhoods in algebraic geometry, Valuations, completions, formal power series and related constructions (associative rings and algebras) Motivic cohomology of fat points in Milnor range via formal and rigid geometries
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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 curves of genus at least two; jacobian; torsion points Curves over finite and local fields, Arithmetic ground fields for curves, Jacobians, Prym varieties A note on the ramification of torsion points lying on curves of genus at least 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 family of curves; geometric genus; associated cycle; integral curve A. NOBILE , On Specializations of Curves, II (Arch. Math., Vol. 46, 1986 , p. 279-288); and Correction: Arch. Math., Vol. 48, 1987 , p. 552. MR 87f:14013 | Zbl 0593.14019 Families, moduli of curves (algebraic), Divisors, linear systems, invertible sheaves On specialization of curves. II
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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 projective plane over the finite field; at most two points on a line; cubic; elliptic curves Hirschfeld, J.W.P., Voloch, J.F.: The characterization of elliptic curves over finite fields. J. Aust. Math. Soc. Ser. A 45(2), 275--286 (1988) Finite ground fields in algebraic geometry, Other finite nonlinear geometries The characterization of elliptic 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 number of primitive points; elliptic curves over number fields Voloch, J. F.: Primitive points on constant elliptic curves over function fields. Bol. soc. Bras. mat. 21, No. 1, 91-94 (1990) Elliptic curves, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Primitive points on constant elliptic curves over function fields
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; rational points; sequences of consecutive squares Rational points, Special sequences and polynomials Sequences of consecutive squares on quartic elliptic curves
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Witten theory; quantum cohomology theory; Gromov-Witten invariants; higher-order-contact curves; quintic threefold A Gathmann, Gromov-Witten and degeneration invariants: computation and enumerative significance, PhD thesis, University of Hannover (1998) Families, moduli of curves (algebraic), Topological properties in algebraic geometry, Special varieties, Special algebraic curves and curves of low genus, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Quantization in field theory; cohomological methods Gromov-Witten- and degeneration invariants: Computation and enumerative significance
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli of complex elliptic curves; decorations Gergondey, R.: Decorated elleptic curves: modular aspects. In: Waldschmidt, M., et al. (eds.) From Number Theory to Physics, 2nd edn., pp. 292--312. Springer, Berlin (1995) Elliptic curves, Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Elliptic curves over global fields Decorated elliptic curves: Modular aspects
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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 computational complexity; algebraic geometry; irreducible polynomials; primitive polynomials; finite fields; polynomial factorization; distribution of primitive polynomials; construction of bases; algebraic number theory; computer science; coding theory; cryptography; factorization of bivariate polynomials; fast algorithms; discrete logarithm problem; fast exponentiation; polynomial multiplication; algebraic curves over finite fields; strengthening of the Weil-Serre bound; rational points; elliptic curves; distribution of primitive points; linear recurring sequences; automata; integer factorization; computational algebraic number theory; algebraic complexity theory; polynomials with integer coefficients 20.I. E. Shparlinski, \(Computational and algorithmic problems in finite fields\), Kluwer, Dordtrecht-Boston-London, 1992. Finite fields and commutative rings (number-theoretic aspects), Research exposition (monographs, survey articles) pertaining to number theory, Number-theoretic algorithms; complexity, Polynomials over finite fields, Arithmetic theory of polynomial rings over finite fields, Algebraic coding theory; cryptography (number-theoretic aspects), Analysis of algorithms and problem complexity, Geometric methods (including applications of algebraic geometry) applied to coding theory, Cryptography, Algebraic number theory computations, Rational points, Curves over finite and local fields Computational and algorithmic problems in 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 number of elliptic curves; \(j\)-invariant Ionel, E, Genus-one enumerative invariants in \(\mathbb{P}^n\) with fixed j-invariant, Duke Math. J., 94, 279-324, (1998) Enumerative problems (combinatorial problems) in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Genus \(1\) enumerative invariants in \(\mathbb{P}^n\) with fixed \(j\) invariant
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomological field theory; Gromov-Witten invariants; tautological cohomology classes; moduli spaces of stable curves; large phase space Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Families, moduli of curves (algebraic), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Relationships between algebraic curves and physics Intersection numbers on the moduli spaces of stable maps in genus 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 cohomology group; action of an automorphism of order p; connected complete non-singular curves; tamely ramified Galois coverings; Witt vector ring Shōichi Nakajima, Action of an automorphism of order \? on cohomology groups of an algebraic curve, J. Pure Appl. Algebra 42 (1986), no. 1, 85 -- 94. Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients), Classical real and complex (co)homology in algebraic geometry Action of an automorphism of order p on cohomology groups of an algebraic curve
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve; group of 0-cycles; Flach's finiteness theorem; Selmer group; complex multiplication; higher \(p\)-adic Abel-Jacobi map A. Langer and W. Raskind, 0-cycles on the selfproduct of a CM-elliptic curve over \(\Q\), J. Reine Angew. Math. 516 (1999), 1--26. Varieties over global fields, Elliptic curves over global fields, Complex multiplication and moduli of abelian varieties, (Equivariant) Chow groups and rings; motives 0-cycles on the self-product of a CM elliptic curve over \(\mathbb{Q}\)
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Quantum cohomology; quantum homology; enumerative geometry; theoretical physics; moduli space of stable maps; Gromov-Witten invariants; Chow ring P. Aluffi ed., \textit{Quantum cohomology at the Mittag-Leffler institute}, Edizioni della Normale, Italy, (1998). Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Proceedings, conferences, collections, etc. pertaining to quantum theory, Collections of articles of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Relationships between surfaces, higher-dimensional varieties, and physics, Quantization in field theory; cohomological methods Quantum cohomology at the Mittag-Leffler Institute
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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 number of distinct elliptic curves; finite field; Edwards curves Rezaeian Farashahi R, Shparlinski I E. On the number of distinct elliptic curves in some families. Designs, Codes and Cryptography, 2010, 1: 83--99 Curves over finite and local fields, Elliptic curves over global fields, Applications to coding theory and cryptography of arithmetic geometry On the number of distinct elliptic curves in some families
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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic cycles; higher Chow groups; higher regulators; variation of Hodge structures; \(K3\) surfaces Algebraic cycles, Transcendental methods, Hodge theory (algebro-geometric aspects), Variation of Hodge structures (algebro-geometric aspects), \(K3\) surfaces and Enriques surfaces, Calabi-Yau manifolds (algebro-geometric aspects), Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) Limits and singularities of normal 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 quadratic forms; function field of a quadric; Pfister forms; Pfister neighbor; Galois cohomology; unramified cohomology; Voevodsky's motivic cohomology; Chow group B. KAHN - R. SUJATHA, Motivic cohomology and unramified cohomology of quadrics. J. Eur. Math. Soc. (JEMS), 2 no. 2 (2000), pp. 145-177. Zbl1066.11015 MR1763303 Quadratic forms over general fields, Quadratic spaces; Clifford algebras, Galois cohomology, Étale and other Grothendieck topologies and (co)homologies, Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Motivic cohomology and unramified cohomology of 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 toric Deligne-Mumford stack; integral Chow ring; Stanley-Reiser ring of stacky fan Jiang, Y.; Tseng, H. -H.: The integral (orbifold) Chow ring of toric Deligne-Mumford stacks. Math. Z. 264, 225-248 (2010) (Equivariant) Chow groups and rings; motives, Generalizations (algebraic spaces, stacks) The integral (orbifold) Chow ring of toric Deligne-Mumford stacks
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cycle index; cohomology; moduli space; real genus \(0\) curves Rains, Eric M., The action of \(S_n\) on the cohomology of \(\overline M_{0,n}(\mathbb{R})\), Selecta Math. (N.S.), 15, 1, 171-188, (2009) Families, moduli of curves (algebraic), Representations of finite symmetric groups, Homotopy theory and fundamental groups in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Real algebraic and real-analytic geometry The action of \(S_n\) on the cohomology of \(\overline{M}_{0,n}(\mathbb{R})\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm E.V. Flynn and N.P. Smart, Canonical heights on the Jacobians of curves of genus 2 and the infinite descent, Acta Arith., 79 (1997), 333-352. MR 98f:11066 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 of the mapping class group; orientable surfaces; characteristic classes; Mumford-Morita-Miller classes Kawazumi, N., Morita, S.: The primary approximation to the cohomology of the moduli space of curves and cocycles for the Mumford-Morita-Miller classes. http://kyokan.ms.u-tokyo.ac.jp/users/preprint/pdf/2001-13.pdf (\textbf{Preprint}) Families, moduli of curves (algebraic), Characteristic classes and numbers in differential topology, (Co)homology theory in algebraic geometry The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable characteristic classes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; Tate-Shafarevich group; homotopy limit problem; motivic cohomology; etale cohomology Elliptic curves over global fields, Motivic cohomology; motivic homotopy theory, Elliptic curves On the arithmetic of elliptic curves and a homotopy limit problem
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 Galois extensions; Galois group; rational curves; division points; elliptic curves; Chebotarev density theorem Asada, M.: Construction of certain non-solvable unramified Galois extensions over the total cyclotomic field. J. fac. Sci. univ. Tokyo sect. IA math. 32, 397-415 (1985) Galois theory, Cyclotomic extensions, Elliptic curves, Rational points Construction of certain non-solvable unramified Galois extensions over the total cyclotomic 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 non-vanishing of \(L\)-functions; twisted \(L\)-functions of elliptic curves; function fields; elliptic curve rank in extensions Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic ground fields for curves On the vanishing of twisted \(L\)-functions of elliptic curves over rational 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 motivic homotopy theory; slice filtration; motivic cohomology; algebraic \(K\)-theory; Hermitian \(K\)-theory; higher Witt-theory; quadratic forms over rings of integers; special values of Dedekind \(\zeta \)-functions of number fields \(K\)-theory of global fields, Zeta functions and \(L\)-functions of number fields, Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) Hermitian \(K\)-theory, Dedekind \(\zeta \)-functions, and quadratic forms over rings of integers in 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 curve; finite field; modular form; moduli of curves; cohomology Geer, G., Counting curves over finite fields, Finite Fields and Appl., 32, 207, (2015) Curves over finite and local fields, Finite ground fields in algebraic geometry, Families, moduli of curves (algebraic) Counting 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 moduli of curves; tautological ring; intersection theory; double ramification cycle Families, moduli of curves (algebraic), Software, source code, etc. for problems pertaining to algebraic geometry admcycles -- a Sage package for calculations in the tautological ring 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 holomorphic mapping of compact Kähler manifold; local Torelli theorem; bundle of elliptic curves Transcendental methods, Hodge theory (algebro-geometric aspects), Period matrices, variation of Hodge structure; degenerations, Families, moduli of curves (algebraic) Local Torelli theorem for bundles on manifolds with \(K=0\)
| 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 character variety; Hodge-Deligne polynomial; E-polynomial; parabolic Higgs bundles; doubly periodic instantons; representations of fundamental group; punctured curves Algebraic moduli problems, moduli of vector bundles, Transcendental methods, Hodge theory (algebro-geometric aspects), Geometric invariant theory Hodge polynomials of the \(\mathrm{SL}(2,\mathbb{C})\)-character variety of an elliptic curve with two marked 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 rank of elliptic curves; function field; multiplicative order Elliptic curves, Algebraic functions and function fields in algebraic geometry, Distribution of integers with specified multiplicative constraints, Class field theory Rank statistics for a family of elliptic curves over a function field
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves conductor 11; parametrization of elliptic curves by modular functions; isogeny class; diophantine equation; Taniyama-Weil conjecture Agrawal, M. K.; Coates, J. H.; Hunt, D. C.; van der Poorten, A. J., Elliptic curves of conductor \(11\), Math. Comp., 35, 151, 991-1002, (1980) Elliptic curves over global fields, Cubic and quartic Diophantine equations, Special algebraic curves and curves of low genus Elliptic curves of conductor 11
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Bogomolov conjecture; curves of higher genus; function fields; metric graphs Faber, X. W. C., The geometric Bogomolov conjecture for curves of small genus, Experiment. Math., 1058-6458, 18, 3, 347\textendash 367 pp., (2009) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic varieties and schemes; Arakelov theory; heights, Heights The geometric Bogomolov conjecture for curves of small genus
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves isogeny class of Abelian varieties; product of simple Abelian varieties; self-product of an elliptic curve Schoen, C., \textit{produkte abelscher varietäten und moduln über ordnungen}, J. Reine Angew. Math., 429, 115-123, (1992) Isogeny, Algebraic theory of abelian varieties, Elliptic curves Products of abelian varieties and modules over orders
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves toric varieties; cone structure; resolution of singularities; fundamental groups; Euler characteristics; cohomology of line bundles; tangent bundle; Serre duality; Betti numbers; Chow groups; cohomology groups W. Fulton, \textit{Introduction to toric varieties}, Annals of Mathematics Studies, Princeton University Press, Princeton U.S.A. (1993). Toric varieties, Newton polyhedra, Okounkov bodies, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Singularities of surfaces or higher-dimensional varieties, Group actions on varieties or schemes (quotients), Homotopy theory and fundamental groups in algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Polyhedra and polytopes; regular figures, division of spaces Introduction to toric varieties. The 1989 William H. Roever lectures in 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 moduli of curves; tautological ring; double ramification cycle Families, moduli of curves (algebraic) A conjectural formula for \(\mathrm{DR}_g(a,-a)\lambda_g\)
| 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 generalized Cartan matrix; Kac-Moody Lie algebras; Kac-Moody groups; projective normality of Schubert varieties; tensor product of two G- modules O. Mathieu : Construction du groupe associé aux algèbres de Kac-Moody . Comptes Rendus 306 série I (1988) 227-230. Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Group schemes, Infinite-dimensional Lie groups and their Lie algebras: general properties Construction du groupe de Kac-Moody et applications. (Construction of the Kac-Moody group with 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 stacks; moduli of curves; equivariant cohomology Edidin, D., Equivariant geometry and the cohomology of the moduli space of curves, (Handbook of Moduli. Vol. I, Adv. Lect. Math. (ALM), vol. 24, (2013), Int. Press Somerville, MA), 259-292 Research exposition (monographs, survey articles) pertaining to algebraic geometry, Stacks and moduli problems, Families, moduli of curves (algebraic), (Equivariant) Chow groups and rings; motives Equivariant geometry and the cohomology of the moduli space 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; rationality questions; special divisors; Brill-Noether theory; unirational varieties; varieties of general type; Koszul cohomology; \(K3\) surfaces \textsc{G. Farkas}, Birational aspects of the geometry of \(M_{g}\), In: Surveys in Differential Geometry. Vol. XIV. Geometry of Riemann Surfaces and Their Moduli Spaces, 57--110 Surv. Differ. Geom., vol. 14, Int. Press, Somerville, MA, 2009 Families, moduli of curves (algebraic), Rationality questions in algebraic geometry, Special divisors on curves (gonality, Brill-Noether theory), Divisors, linear systems, invertible sheaves, Picard groups, \(K3\) surfaces and Enriques surfaces Birational aspects of the geometry of \(\overline{\mathcal M}_g\)
| 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 Galois cohomology; \(K\)-cohomology; motivic complex; Galois covering; action of Galois group; equivariant Chow group; totally \(k\)-negligible classes Peyre, E.: Application of motivic complexes to negligible classes. In: Algebraic K-theory, Raskind, W., Weibel, C., eds., (Seattle, 1997) Proc. Symp. Pure Math., vol. 67, pp. 181--211. AMS, Providence (1999) Motivic cohomology; motivic homotopy theory, Group actions on varieties or schemes (quotients), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Higher symbols, Milnor \(K\)-theory, (Equivariant) Chow groups and rings; motives Application of motivic complexes to negligible classes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves constructions and bounds for codes; three-way channel; random-coding techniques; two-way channel; binary adder two-access channel; concatenation techniques; Manhattan-distance; codes from Hermitian curves Linear codes (general theory), Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry Constructing codes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves specializations of elliptic quartic curves; Grassmannian of pencils of quadrics Israel Vainsencher and Dan Avritzer, Compactifying the space of elliptic quartic curves, Complex projective geometry (Trieste, 1989/Bergen, 1989) London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 47 -- 58. Families, moduli of curves (algebraic), Elliptic curves, Grassmannians, Schubert varieties, flag manifolds Compactifying the space of elliptic quartic 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 cusp forms; periods of a newform; algorithms; modular elliptic curves; computations Cremona J., Experiment. Math. pp 97-- (1997) Elliptic curves over global fields, Holomorphic modular forms of integral weight, Computational aspects of algebraic curves, Number-theoretic algorithms; complexity Computing periods of cusp forms and 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 \(l\)-adic Abel-Jacobi map; group of codimension-\(n\) cycles modulo rational equivalence; filtration; \(l\)-adic étale cohomology; cycle map; function field in one variable W. Raskind, ''Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow groups,'' Duke Math. J., vol. 78, iss. 1, pp. 33-57, 1995. Algebraic cycles, Local ground fields in algebraic geometry, Parametrization (Chow and Hilbert schemes), Étale and other Grothendieck topologies and (co)homologies Higher \(l\)-adic Abel-Jacobi mappings and filtrations on Chow groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves non-Archimedean Riemann-Roch theorem; non-Archimedean analogue of Arakelov theory; operational Chow-cohomology S. Bloch, H. Gillet, and C. Soulé, Non-Archimedean Arakelov theory, J. Algebraic Geom. 4 (1995), no. 3, 427 -- 485. Arithmetic varieties and schemes; Arakelov theory; heights, Local ground fields in algebraic geometry Non-archimedean Arakelov theory
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Bibliography; L-functions; regulators; algebraic cycles; Deligne-Beilinson cohomology; Yoneda extensions; mixed motives; Pell's equation; Dedekind's class number; Taylor series; Hodge conjecture; Tate's conjecture; polylogarithms; variations of mixed Hodge structures; generalized Hodge group; Birch and Swinnerton-Dyer conjectures; arithmetic varieties D. Ramakrishnan, Regulators, algebraic cycles, and values of \(L\)-functions , Algebraic \(K\)-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 183-310. Applications of methods of algebraic \(K\)-theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), (Co)homology theory in algebraic geometry, Zeta functions and \(L\)-functions of number fields Regulators, algebraic cycles, and values of L-functions
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves modular elliptic curve; cohomology classes; invariants of Selmer groups Kolyvagin, V.A.: On the structure of Selmer groups. Math. Ann. 291(2) (1991) Elliptic curves over global fields, Elliptic curves, Families, moduli of curves (algebraic), Rational points, Class numbers, class groups, discriminants On the structure of Selmer 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 threefolds; pencil of del Pezzo surfaces; exceptional curves; Prym-Tyurin variety; intermediate Jacobian; Chow group Kanev V., Intermediate Jacobians and Chow groups of threefolds with a pencil of del Pezzo surfaces, Ann. Mat. Pura Appl., 1989, 154, 13--48 Picard schemes, higher Jacobians, Parametrization (Chow and Hilbert schemes), \(3\)-folds, Jacobians, Prym varieties Intermediate Jacobians and Chow groups of threefolds with a pencil of del Pezzo 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 representation theory; reductive algebraic groups; simple G-modules; highest weights; character formula; Weyl's formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology ring; ring of regular functions; Schubert schemes; line bundles [6] Jantzen J.\ C., Representations of Algebraic Groups, Academic Press, Orlando, 1987 Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Research exposition (monographs, survey articles) pertaining to group theory, Group schemes, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over arbitrary fields Representations of algebraic groups
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves chiral homology of elliptic curves; quasiconformal vertex algebra; Hochschild homology of Zhu algebra Vertex operators; vertex operator algebras and related structures, Elliptic curves Chiral homology of elliptic curves and the Zhu algebra
| 0 |
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