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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 zero estimates; arithmetic of abelian varieties; abelian integrals; Baker's method; Siegel's theorem; effective estimate for isogenies; 1- motives; isogenies between elliptic curves; Philippon's fundamental multiplicity estimate D. Bertrand, Transcendental methods in arithmetic geometry , Analytic number theory (Tokyo, 1988), Lecture Notes in Math., vol. 1434, Springer, Berlin, 1990, pp. 31-44. Linear forms in logarithms; Baker's method, Arithmetic ground fields for abelian varieties, Rational points Transcendental methods in arithmetic 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 Manin constant; Stickelberger element; modular parametrizations of elliptic curves Families, moduli of curves (algebraic), Elliptic curves, Arithmetic ground fields for abelian varieties On the periods of 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 pencil of elliptic curves; hyperelliptic curves; connectedness of regular surfaces of general type; fundamental group of a surface Xiao, G., \textit{\({\pi}\)_{1} of elliptic and hyperelliptic surfaces}, Internat. J. Math., 2, 599-615, (1991) Homotopy theory and fundamental groups in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Topological properties in algebraic geometry, Families, moduli of curves (algebraic) \({\pi{}}_ 1\) of elliptic and hyperelliptic 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 étale cohomology; algebraic cycles; motivic cohomology; higher Chow groups Étale and other Grothendieck topologies and (co)homologies, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), (Equivariant) Chow groups and rings; motives An isomorphism by Suslin
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; graphics processing unit; modular arithmetic; elliptic curves; elliptic-curve method of factorization; Edwards curves Daniel J. Bernstein, Tien-Ren Chen, Chen-Mou Cheng, Tanja Lange, and Bo-Yin Yang, ECM on graphics cards, Advances in cryptology --- EUROCRYPT 2009, Lecture Notes in Comput. Sci., vol. 5479, Springer, Berlin, 2009, pp. 483 -- 501. Cryptography, Factorization, Applications to coding theory and cryptography of arithmetic geometry, Symbolic computation and algebraic computation ECM on graphics cards
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves pencil of curves; surfaces of general type; irregularity one; canonical mapping; resolution of an irreducible relative quartic hypersurface; locally free sheaves; elliptic curves T. TAKAHASHI, Certain algebraic surfaces of general type with irregularity one and their canonica mappings, Tohoku Mathematical Publications 2 (1996), 1-60 Surfaces of general type, Research exposition (monographs, survey articles) pertaining to algebraic geometry Certain algebraic surfaces of general type with irregularity one and their canonical mappings
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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-torsion in elliptic curves; cyclotomic field; G-curve; non-existence of non-cuspidal rational points --. --. --. --., \(p\)-torsion in elliptic curves over subfields of \(\mathbf{Q}(\mu_p)\) , Math. Ann. 280 (1988), 513--519. Arithmetic ground fields for curves, Rational points, Elliptic curves, Special algebraic curves and curves of low genus, Cyclotomic extensions p-torsion in elliptic curves over subfields of \({\mathbb Q}(\mu _ p)\)
| 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 Galois structure; elliptic curves; Hopf orders; principal homogeneous space; explicit determination of generators; group schemes; \(p\)-adic \(L\)-function of an elliptic curve; elliptic units; Picard invariant Cassou-Noguès, Structures galoisiennes et courbes elliptiques, J. Théor. Nombres Bordeaux 7 pp 307-- (1995) Integral representations related to algebraic numbers; Galois module structure of rings of integers, Elliptic curves over global fields, Group schemes Galois structure and elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves isomorphism classes of elliptic curves; rational point of order p; finite Mordell-Weil group Kamienny, S, Torsion points on elliptic curves over all quadratic fields. duke, Math. J, 53, 157-162, (1986) Special algebraic curves and curves of low genus, Rational points, Quadratic extensions, Arithmetic ground fields for curves, Elliptic curves, Jacobians, Prym varieties Torsion points on elliptic curves over all quadratic fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; elliptic integrals; geometric realization of addition law; plane quartics Elliptic curves, Elliptic functions and integrals A geometric approach to Euler's addition formula
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Vinberg representation; arithmetic invariant theory; Galois cohomology; arithmetic of the Jacobian of algebraic curves Thorne, J. A., \textit{vinberg's representations and arithmetic invariant theory}, Algebra Number Theory, 7, 2331-2368, (2013) Galois cohomology of linear algebraic groups, Linear algebraic groups over global fields and their integers, Geometric invariant theory Vinberg's representations and arithmetic invariant 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 Poincaré-Serre polynomials; moduli spaces of curves; cohomology; symmetric polynomials Bergström, J; Minabe, S, On the cohomology of the Losev-Manin moduli space, Manuscr. Math., 144, 241-252, (2014) Families, moduli of curves (algebraic), Toric varieties, Newton polyhedra, Okounkov bodies On the cohomology of the Losev-Manin moduli space
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves moduli space of stable genus two curves with a level structure; rationality of the moduli space Lee, R. and Weintraub, S. , Moduli spaces of Riemann surfaces of genus two with level structures . I. Math. Gottingensis. 66 (1986), to appear in Trans. AMS, 1988. Families, moduli of curves (algebraic), Families, moduli of curves (analytic), Compactification of analytic spaces, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Cohomology of arithmetic groups, Arithmetic aspects of modular and Shimura varieties Moduli spaces of Riemann surfaces of genus two with level structures. I
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves motives; review of Iwasawa main conjecture; cyclotomic fields; elliptic curves; Selmer group; cyclotomic deformations of motives R. Greenberg, ''Iwasawa theory and \(p\)-adic deformations of motives,'' in Motives, II (Seattle, WA, 1991), Proc. Sympos. Pure Math. 55, Amer. Math. Soc., Providence, 1994, 193--223. Iwasawa theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Generalizations (algebraic spaces, stacks), Research exposition (monographs, survey articles) pertaining to number theory Iwasawa theory and \(p\)-adic deformations of motives
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves average rank of families of elliptic curves with polynomial of coefficients; Sato-Tate measure; distribution the number of rational points Michel Philippe, Monatshefte für Mathematik 120 pp 127-- (1995) Elliptic curves over global fields, Elliptic curves Average rank of families of elliptic curves and Sato-Tate laws
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Theorems of Pascal and Brianchon; extension; plane curves; surfaces of the third order; Cartesian higher geometriy; conjugated polygons; inscribed into a curve; conic section Desarguesian and Pappian geometries, Euclidean geometries (general) and generalizations, Plane and space curves, Families, moduli, classification: algebraic theory, Curves in Euclidean and related spaces, Polyhedra and polytopes; regular figures, division of spaces, Euclidean analytic geometry Note on extending the theorems of Pascal and Brianchon to the plane curves and to the surfaces of \(3^rd\) class.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Artin conjecture; Kloosterman sum conjecture; functional equations; Sato-Tate conjecture; elliptic curves; Eisenstein series; Calabi-Yau varieties; zeta-functions; modular forms; Hecke operators; new forms; representations of Galois groups; automorphic forms of \(\text{GL}_2\) \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Varieties over global fields, Hecke-Petersson operators, differential operators (one variable), Calabi-Yau manifolds (algebro-geometric aspects), Galois representations, Elliptic curves over global fields, Holomorphic modular forms of integral weight The arithmetic of modular forms
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic stacks; integral Chow ring; hyperelliptic curves of even genus [Ed-Fu2] D. Edidin and D. Fulghesu, The integral Chow ring of the stack of hyperelliptic curves of even genus, Math. Res. Lett. 16 (2009), no. 1, 27--40. (Equivariant) Chow groups and rings; motives, Generalizations (algebraic spaces, stacks), Equivariant homology and cohomology in algebraic topology, Families, moduli of curves (algebraic) The integral Chow ring of the stack of hyperelliptic curves of even 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 constructing elliptic curves of high rank Mestre, JF, Construction de courbes elliptiques sur \(\mathbb{Q}\) de rang \(\geq \)12, C. R. Acad. Sci. Paris Ser., I, 643-644, (1982) Special algebraic curves and curves of low genus, Elliptic curves, Arithmetic ground fields for curves, Software, source code, etc. for problems pertaining to algebraic geometry Construction d'une courbe elliptique de rang \(\geq 12\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves arrangement of subvarieties; characteristic cycle; Betti numbers; local cohomology Josep Àlvarez Montaner, Ricardo García López, and Santiago Zarzuela Armengou, Local cohomology, arrangements of subspaces and monomial ideals, Adv. Math. 174 (2003), no. 1, 35 -- 56. Local cohomology and commutative rings, Special varieties, Local cohomology and algebraic geometry, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) Local cohomology, arrangements of subspaces and monomial ideals.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Tate conjecture; Shafarevich conjecture; algebraic dependence of; meromorphic functions; effective results on isogenies of elliptic curves Chudnovsky, D. V.; Chudnovsky, G. V.: Padé approximations and Diophantine geometry. Proc. natl. Acad. sci. USA 82, 2212-2216 (1985) Algebraic theory of abelian varieties, Transcendence (general theory), Compact analytic spaces, Elliptic curves, Special algebraic curves and curves of low genus Padé approximations and Diophantine 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; Gorenstein singularities; curves of genus two; crimping spaces Families, moduli of curves (algebraic), Singularities of curves, local rings, Special algebraic curves and curves of low genus Modular compactifications of \(\mathcal{M}_{2,n}\) with Gorenstein 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 crystalline cohomology; higher Chern class; syntomic sheaf; p-adic regulator; values of p-adic L-function Gros, Michel, Régulateurs syntomiques et valeurs de fonctions \(L\) \(p\)-adiques. I, with an appendix by Masato Kurihara, Invent. Math., 99, 2, 293-320, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, \(p\)-adic cohomology, crystalline cohomology, Local ground fields in algebraic geometry Syntomic regulators and values of \(p\)-adic \(L\)-functions. I. Appendix by Masato Kurihara
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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-Roch-Grothendieck; existence of a good cycle class map into crystalline cohomology; Weil cohomology theory H. GILLET - W. MESSING, Cycle classes and Riemann Roch for crystalline cohomology, Duke 55(3) (1987), pp. 501-538. Zbl0651.14014 MR904940 \(p\)-adic cohomology, crystalline cohomology, Riemann-Roch theorems, Cycles and subschemes Cycle classes and Riemann-Roch for crystalline 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 products of CM elliptic curves; Coleman's conjecture; endomorphism algebras; singular abelian surfaces Arithmetic aspects of modular and Shimura varieties, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties Endomorphism algebras of geometrically split abelian surfaces over \(\mathbb{Q} \)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves pencil of plane cubics; canonical class of a surface; Noether's formula; del Pezzo surfaces; rational elliptic surfaces; configurations; quotients of the two-dimensional unit ball I. Naruki, \textit{Configurations related to maximal rational elliptic surfaces}, \textit{Adv. Stud. Pure Math.}\textbf{8} (1986) 315. Special surfaces, Families, moduli, classification: algebraic theory, Projective techniques in algebraic geometry, Elliptic curves, Rational and unirational varieties Configurations related to maximal rational elliptic 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 Courbes elliptiques; Séminaire; Mordell effectif; Paris (France); bundles of elliptic curves Szpiro, L.: Séminaire sur LES pinceaux de courbes elliptiques (à la recherche de ''Mordell effectif ''). Astérisque 183 (1990) Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry Séminaire sur les pinceaux de courbes elliptiques (à la recherche de ``Mordell effectif''), tenu en 1988 à l'Institut Henri Poincaré á Paris, France
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves regular log schemes; extension of maps; stable curves; Deligne-Mumford stack; coarse moduli space; hyperbolic polycurves Arbarello, E., Cornalba, M., Griffiths, P.A.: Geometry of Algebraic Curves, II. Grundlehren der mathematischen Wissenschaften \textbf{268}. Springer, Berlin (2011) Families, moduli of curves (algebraic), Toric varieties, Newton polyhedra, Okounkov bodies Extending families of curves over log regular schemes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 that admit degree covers of an elliptic curve; one-parameter family of simply branched covers; moduli space of stable genus curves Dawei Chen, ``Covers of elliptic curves and the moduli space of stable curves'', J. Reine Angew. Math.649 (2010), p. 167-205 Elliptic curves, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Algebraic moduli problems, moduli of vector bundles Covers of elliptic curves and 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 congruent number problem; Heegner points; arithmetic of elliptic curves; algorithms for finding rational points Noam D. Elkies, Heegner point computations, Algorithmic number theory (Ithaca, NY, 1994) Lecture Notes in Comput. Sci., vol. 877, Springer, Berlin, 1994, pp. 122 -- 133. Computational aspects of algebraic curves, Elliptic curves, Elliptic curves over global fields, Algebraic number theory computations, Rational points Heegner point computations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher Chow groups; rational curves; abelian surfaces Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Varieties over finite and local fields, (Equivariant) Chow groups and rings; motives, Local ground fields in algebraic geometry Higher Chow cycles on abelian surfaces and a non-Archimedean analogue of the Hodge-\(\mathcal{D}\)-conjecture
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves stably integral points on elliptic curves; number of integral points Patricia L. Pacelli, Uniform bounds for stably integral points on elliptic curves, Proc. Amer. Math. Soc. 127 (1999), no. 9, 2535 -- 2546. Rational points, Elliptic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Uniform bounds for stably integral points on elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves complete intersection; Chow ring of the moduli space of stable curves of genus 4; tautological class Carel Faber, Chow rings of moduli spaces of curves. I. The Chow ring of \overline{\Cal M}\(_{3}\), Ann. of Math. (2) 132 (1990), no. 2, 331 -- 419. , https://doi.org/10.2307/1971525 Carel Faber, Chow rings of moduli spaces of curves. II. Some results on the Chow ring of \overline{\Cal M}\(_{4}\), Ann. of Math. (2) 132 (1990), no. 3, 421 -- 449. Families, moduli of curves (algebraic), Parametrization (Chow and Hilbert schemes), Structure of families (Picard-Lefschetz, monodromy, etc.), Algebraic moduli problems, moduli of vector bundles Chow rings of moduli spaces of curves. II: Some results on the Chow ring of \(\overline{{\mathcal M}_ 4}\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves bordered elliptic-hyperelliptic Klein surfaces; real algebraic curves; discrete isometry groups of the hyperbolic plane; order of the automorphism group Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients), Other geometric groups, including crystallographic groups, Real algebraic and real-analytic geometry Elliptic-hyperelliptic Klein 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 modularity of algebraic curve; modular curve; singular moduli; elliptic curves with complex multiplication André, Yves, Finitude des couples d'invariants modulaires singuliers sur une courbe algébrique plane non modulaire, J. Reine Angew. Math.. Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], 505, 203-208, (1998) Modular and Shimura varieties, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Elliptic curves, Transcendence (general theory), Elliptic curves over global fields Finiteness of couples of singular modular invariants on a plane non-modular algebraic curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Higher geometry; Plücker and Jacobi; theorems of Pascal and Desargues; space curves of \(3^rd\) and \(4^th\) degree; to construct a cone; directrix; apex; common points; intersection of surface of \(2^nd\) order Configuration theorems in linear incidence geometry, Plane and space curves, Desarguesian and Pappian geometries, Curves in Euclidean and related spaces, Structure of proofs, Rational and ruled surfaces, Surfaces in Euclidean and related spaces Note on some theorems of higher 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 Wieferich's criterion; first case of Fermat's last theorem; abc- conjecture; points of infinite order; elliptic curves; j-invariants Silverman, Joseph H., Wieferich's criterion and the \(abc\)-conjecture, J. Number Theory, 30, 2, 226-237, (1988) Higher degree equations; Fermat's equation, Elliptic curves Wieferich's criterion and the abc-conjecture
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves rational elliptic surfaces of index two; toric GIT quotient; moduli space Algebraic moduli problems, moduli of vector bundles, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Elliptic surfaces, elliptic or Calabi-Yau fibrations The moduli space of rational elliptic surfaces of index two
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Matsumoto-Montesino's theory; automorphisms of surfaces; monodromy; degeneration of curves; monodromies of degenerations; elliptic families Families, moduli of curves (algebraic), Fibrations, degenerations in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves Monodromies of hyperelliptic families of genus three 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 toric degeneration; Chow quotient; moduli of curves Fibrations, degenerations in algebraic geometry, Group actions on varieties or schemes (quotients), Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Birational geometry, Toric varieties, Newton polyhedra, Okounkov bodies Toric degenerations of GIT quotients, Chow quotients, and \(\overline {M}_{0,n}\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves homology of modular curves; modular parametrizations of elliptic curves; winding number; Mordell-Weil group; first singular homology group; Hecke operators; representation of the homology Merel, L.: Homologie des courbes modulaires affines et paramétrisations modulaires. Ser. number theory, 110-130 (1995) Elliptic curves over global fields, Hecke-Petersson operators, differential operators (one variable), Elliptic curves Homology of affine modular curves and modular parametrization
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; complex multiplication; L-function; motivic cohomology; regulator map; Deligne cohomology Applications of methods of algebraic \(K\)-theory in algebraic geometry, Complex multiplication and abelian varieties, Elliptic curves, Relations of \(K\)-theory with cohomology theories, \(K\)-theory of schemes Higher regulators 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 elliptic curves over function fields; Tate-Shafarevich groups; explicit computation of \(L\)-functions; BSD conjecture; Gauss and Kloosterman sums Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Gauss and Kloosterman sums; generalizations Elliptic curves with large Tate-Shafarevich groups over \(\mathbb{F}_q(t)\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves stable curves; stable maps; enumerative problems; Kontsevich formula; Gromov-Witten invariants; quantum cohomology; quantum product; generating function Kock, J.; Vainsencher, I., An invitation to quantum cohomology. Kontsevich's formula for rational plane curves, Progress in Mathematics, vol. 249, (2007), Birkhäuser Boston, Inc. Boston, MA Research exposition (monographs, survey articles) pertaining to algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Enumerative problems (combinatorial problems) in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds An invitation to quantum cohomology. Kontsevich's formula for rational plane curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Iwasawa theory; supersingular reduction; Tate-Shafarevich group; p-adic L-function; Selmer groups; ring of norms; p-adic heights; supersingular elliptic curves Perrin-Riou, Bernadette, Theorie d'Iwasawa \textit{p}-adique locale et globale, Invent. Math., 99, 247-292, (1990) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Elliptic curves Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa 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 motive; motivic cohomology; Chow groups; numerical equivalence of cycles; Milnor's operations (Equivariant) Chow groups and rings; motives, Algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Motivic cohomology; motivic homotopy theory Isotropic motives
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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; \(L-A\) pair; integrability; Hess-Appel'rot system; separation of variables Dragović, V; Gajić, B, Elliptic curves and a new construction of integrable systems, Reg. Chaotic Dyn., 14, 466-478, (2009) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Integrable cases of motion in rigid body dynamics, Elliptic curves Elliptic curves and a new construction of integrable systems
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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; embedding degree; pairing-based cryptography; characters of fields; Jacobi sums DOI: 10.1016/j.cam.2010.08.020 Cryptography, Curves over finite and local fields, Exponential sums, Algebraic coding theory; cryptography (number-theoretic aspects), Elliptic curves On the elliptic curves \(y^{2}=x^{3} - c\) with embedding degree one
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves unipotent sheaves; an elliptic analogue of the polylogarithm; motivic cohomology classes; regulator A. Beilinson and A. Levin, \textit{The Elliptic Polylogarithm}, in \textit{Motives}, U. Jannsen, S. Kleiman and J.-P. Serre eds., \textit{Proc. Symp. Pure Math.}\textbf{55} (1994) 123, Part 2, AMS (1994). Elliptic curves, Elliptic curves over global fields, Generalizations (algebraic spaces, stacks), Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry The elliptic polylogarithm
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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 and hyperelliptic curves; discrete logarithm; point counting; realization of discrete logarithm systems H. Cohen and G. Frey, \textit{Handbook of Elliptic and Hyperelliptic Curve Cryptography}, Chapman & Hall/CRC, Boca Raton, FL, 2005. General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to information and communication theory, Cryptography, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry, Number-theoretic algorithms; complexity, Factorization, Primality Handbook of elliptic and hyperelliptic curve cryptography.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; invariant theory; higher secant varieties Elliptic curves over global fields, Syzygies, resolutions, complexes and commutative rings, Elliptic curves A formula for the Jacobian of a genus one curve of arbitrary degree
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Koszul cohomology; gonality; Clifford index; syzygy; syzygies of curves Special divisors on curves (gonality, Brill-Noether theory), Syzygies, resolutions, complexes and commutative rings, Plane and space curves, Vector bundles on curves and their moduli Geometry of curves and Koszul 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 isomorphism of elliptic curves; rational point of order p Kamienny, S, Torsion points on elliptic curves over all quadratic fields. II., Bull. Soc. Math. France, 114, 119-122, (1986) Special algebraic curves and curves of low genus, Quadratic extensions, Rational points, Arithmetic ground fields for curves, Elliptic curves Torsion points on elliptic curves over all quadratic fields. 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 crystalline cohomology of higher level; transversal crystals; filtered de Rham complex; group schemes; invariant differential forms \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Group schemes The filtered Poincaré Lemma in higher level (with applications to 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 boundedness conjecture for group of rational torsion points; elliptic curve; Mordell-Weil theorem; abelian variety; potential complex multiplication; torsion points on the Fermat curves; p-adic abelian integrals Coleman, Robert F., Torsion points on curves and \textit{p}-adic abelian integrals, Ann. of Math. (2), 121, 1, 111-168, (1985), MR782557 Analytic theory of abelian varieties; abelian integrals and differentials, Local ground fields in algebraic geometry, Complex multiplication and abelian varieties, Rational points, Special algebraic curves and curves of low genus, Elliptic curves, Algebraic functions and function fields in algebraic geometry, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) Torsion points on curves and p-adic abelian integrals
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 variety; variety of flat connections; cohomology jump loci; analytic germ; differential graded algebra model; quasi-projective manifold; admissible map; Deligne weight filtration; holonomy Lie algebra; semisimple Lie algebra Homotopy theory and fundamental groups in algebraic geometry, Homology with local coefficients, equivariant cohomology, Ordinary representations and characters, Rational homotopy theory, Semisimple Lie groups and their representations, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) Rank two topological and infinitesimal embedded jump loci of quasi-projective manifolds
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves torus action; compactified representation; equivariant homeomorphism; equivariant cohomology; product of spheres; division algebra Franz, M; López de Medrano, S; Malik, J, Mutants of compactified representations revisited, Bol. Soc. Mat. Mex., 23, 511-526, (2017) Groups acting on specific manifolds, Topology of real algebraic varieties, Nonassociative division algebras, Equivariant algebraic topology of manifolds Mutants of compactified representations revisited
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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-Roch formula for \(\ell\)-adic sheaves of rank one; \({\mathcal D}\)-module; invariants of wild ramification; ramification in finite coverings of higher dimensional schemes; Artin characters for higher dimensional regular local rings; class field theory; Serre's conjecture; ramification of Galois representations; Swan conductor; characteristic cycle K. Kato, Class field theory, \(D\)-modules, and ramification on higher-dimensional schemes, Part I, Amer. J. Math., 116, 757-784, (1994) Class field theory, Geometric class field theory, Generalized class field theory (\(K\)-theoretic aspects), Riemann-Roch theorems, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Class field theory, \({\mathcal D}\)-modules, and ramification on higher dimensional schemes. I
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves cohomological invariants; moduli of hyperelliptic curves; Chow groups with coefficients Families, moduli of curves (algebraic), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Stacks and moduli problems, Coverings of curves, fundamental group A complete description of the cohomological invariants of even genus hyperelliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves transcendence of elliptic modular functions in characteristic \(p\); Tate elliptic curve; theorem of Siegel and Schneider; transcendence of periods of elliptic curves; Mahler-Manin conjecture; elliptic logarithm [V1] J. F. Voloch:Transcendence of elliptic modular functions in characteristic p, J. Number Theory58 (1996) 55-59. Transcendence theory of elliptic and abelian functions, Elliptic curves Transcendence of elliptic modular functions in characteristic \(p\)
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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 mirror pairs; mirror symmetry; Calabi-Yau models; enumerative geometry of rational curves; quintic threefold; Gromov-Witten invariants; stable maps; duality theory for toric varieties; quantum differential equations; Kähler cones; Mori cones; variations of Hodge structures; Picard-Fuchs equations; unipotent monodromy; Gauss-Manin connection; equivariant cohomology; terminal singularieties D.A. Cox and S. Katz, \textit{Mathematical surveys and monographs. Vol. 68: Mirror symmetry and algebraic geometry}, AMS, New York U.S.A. (1999). Calabi-Yau manifolds (algebro-geometric aspects), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to quantum theory, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Topological field theories in quantum mechanics, Calabi-Yau theory (complex-analytic aspects), Supersymmetric field theories in quantum mechanics, Toric varieties, Newton polyhedra, Okounkov bodies, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) Mirror symmetry and algebraic geometry
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves iterated mappings; dynamical systems; Coxeter groups; birational transformations; Cremona transformations; inversion relations; Yang- Baxter equations; automorphisms of algebraic varieties; elliptic curves; resonant tori; Plücker variables; quantum integrability; involutions; birational mappings; deformations M.P. Bellon, J.-M. Maillard, C.-M. Viallet, Dynamical systems from quantum integrability, in: J.-M. Maillard (Ed.), Proceedings of the Conference Yang--Baxter Equations in Paris, World Scientific, Singapore, 1993, pp. 95--124, Int. J. Mod. Phys. Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, Rational and birational maps, Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, Automorphisms of surfaces and higher-dimensional varieties Dynamical systems from quantum integrability
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves frequencies of the values of certain ternary Kloosterman sums; isogeny class of elliptic curves; class numbers; weight distribution; codes Katz, Nicholas; Livné, Ron, Sommes de Kloosterman et courbes elliptiques universelles caractéristiques 2 et 3, C. R. Acad. Sci. Paris Sér. I Math., 309, 11, 723-726, (1989) Elliptic curves, Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Class numbers, class groups, discriminants, Isogeny Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. (Kloosterman sums and universal elliptic curves in characteristics 2 and 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 non vanishing of first cohomology group; non complete intersection; curves in projective 3-space Special algebraic curves and curves of low genus, Classical real and complex (co)homology in algebraic geometry, Complete intersections A remark on the cohomology of curves in \({\mathbb{P}}^ 3\)
| 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 elliptic surfaces; principal homogeneous spaces over elliptic curves; genus one fibrations; Tate-Shafarevich group; moduli spaces of genus one fibrations Elliptic surfaces, elliptic or Calabi-Yau fibrations, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic moduli problems, moduli of vector bundles On the geometry of principal homogeneous spaces
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Grothendieck-Riemann-Roch theorem; Deligne-Mumford stack; cohomology with coefficients in representations; equivariant \(K\)-theory; Vistoli's decomposition theorem; étale descent; homological descent; Chow envelope Bertrand Toën, ``Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford'', K-Theory18 (1999) no. 1, p. 33-76 Riemann-Roch theorems Riemann-Roch theorems for 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 Chow groups; Hilbert symbol; elliptic curves; p-adic fields T. Takemoto, Zero-cycles on products of elliptic curves over \(p\)-adic fields, Acta Arith. 149 (2011), no. 3, 201--214. Elliptic curves over local fields, (Equivariant) Chow groups and rings; motives Zero-cycles on products of elliptic curves over \(p\)-adic fields
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves algebraic cycles; Shimura varieties; Eisenstein series; Siegel-Weil formula; explicit description of the cup product of the Betti cohomology classes; modular symbols; intersection numbers; Fourier coefficients Kudla, S., \textit{algebraic cycles on Shimura varieties of orthogonal type}, Duke J. Math., 86, 39-78, (1997) Cohomology of arithmetic groups, Modular and Shimura varieties, Algebraic cycles, Arithmetic aspects of modular and Shimura varieties Algebraic cycles on Shimura varieties of orthogonal type
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves rational curves; multiple points; one-to-one correspondence between lattices of points; fundamental period parallelograms of elliptic functions; absolute invariant Algebraic geometry Curve razionali che esprimono le relazioni modulari
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves complex polynomial in two variables; level curve; bidisk containing the topology of the level curve; critical point; critical value; vanishing cycle; abelian integral; period determinant Glutsyuk, A.: Upper bounds of topology of complex polynomials in two variables. Mosc. Math. J. 5(4), 781--828 (2005) and p. 972. MR2266460 Structure of families (Picard-Lefschetz, monodromy, etc.), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Polynomials and rational functions of one complex variable Upper bounds of topology of complex polynomials in two variables
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves deformations of singularities; hyperplane sections; elliptic partition curves; minimally elliptic surface singularity; number of generators --, Obstructions and hypersurface sections (minimally elliptic singularities).Trans. Amer. Math. Soc. 335 (1993), 175--193. Deformations of singularities, Singularities of surfaces or higher-dimensional varieties, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Complex surface and hypersurface singularities Obstructions and hypersurface sections (minimally elliptic singularities)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves varieties over local fields; Chow groups; algebraic \(K\)-theory; \(p\)-divisible groups; syntomic cohomology; Dieudonné modules; rings of Witt vectors; Artinian algebras Yamazaki, T.: Formal Chow groups, p-divisible groups, and syntomic cohomology. Duke math. J. 102, 359-390 (2000) Local ground fields in algebraic geometry Formal Chow groups, \(p\)-divisible groups and syntomic 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 rational elliptic fibration; moduli; ball quotient; homology of cyclic coverings; central extension of a braid class group; Eisenstein curve; rational curves Gert Heckman and Eduard Looijenga, The moduli space of rational elliptic surfaces, Algebraic geometry 2000, Azumino (Hotaka), Adv. Stud. Pure Math., vol. 36, Math. Soc. Japan, Tokyo, 2002, pp. 185 -- 248. Moduli, classification: analytic theory; relations with modular forms, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Automorphic forms in several complex variables, Coverings of curves, fundamental group The moduli space of rational elliptic 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 curves of third degree; elliptic functions Curves in algebraic geometry, Elliptic functions and integrals On the geometrical interpretation of certain formulae in elliptic functions.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Diophantine inequalities; asymptotic Fermat; survey; Szpiro conjecture; modular height; conductor; elliptic curves; abc conjecture; Hall conjecture; upper bounds on the number of torsion elements; lower bound on the canonical height Lang S 1990 Old and new conjectured diophantine inequalities \textit{Bull. Am. Math. Soc.}23 37--75 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Research exposition (monographs, survey articles) pertaining to number theory, Diophantine inequalities, Higher degree equations; Fermat's equation, Elliptic curves over global fields, Arithmetic ground fields for curves, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Global ground fields in algebraic geometry, Diophantine inequalities, Elliptic curves Old and new conjectured Diophantine inequalities
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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; elliptic curves with complex multiplication; Euler systems; Iwasawa theory of elliptic curves Coates J., Elliptic curves with complex multiplication and Iwasawa theory, Bull. Lond. Math. Soc. 23 (1991), no. 4, 321-350. Elliptic curves over global fields, Iwasawa theory, Elliptic curves, Rational points, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture Elliptic curves with complex multiplication and Iwasawa 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 Galois representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (1989). Arithmetic varieties and schemes; Arakelov theory; heights, Galois theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic surfaces, elliptic or Calabi-Yau fibrations, General ternary and quaternary quadratic forms; forms of more than two variables, Elliptic curves over global fields, Elliptic curves Mordell-Weil lattices and Galois representation. III
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Chow group; Deligne cohomology James D. Lewis, Real regulators on Milnor complexes, \?-Theory 25 (2002), no. 3, 277 -- 298. Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Higher symbols, Milnor \(K\)-theory, Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Real regulators on Milnor complexes
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves semistable \(\ell\)-adic representation of the Galois group; Weil-Delique group; Deligne module; characteristic \(p\); \(\ell\)-adic étale cohomology Fontaine, J.-M., Représentations \textit{\(\mathcal{l}\)}-adiques potentiellement semi-stables, Astérisque, 223, 321-347, (1994) \(p\)-adic cohomology, crystalline cohomology, Local ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Drinfel'd modules; higher-dimensional motives, etc. Potentially semi-stable \(\ell\)-adic representations
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves textbook (algebraic geometry); problem book; conics; elliptic curves; affine varieties; projective varieties; plane projective curves; sheaves; cohomology; Riemann-Roch theorem Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Varieties and morphisms, Special algebraic curves and curves of low genus, Elliptic curves, Sheaf cohomology in algebraic topology, Plane and space curves, Problem books, Comprehensive works on geometry education Algebraic geometry. A problem solving approach
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves singularity of space curves; postulation deficiency; liaison; cohomology of the normal bundles of the linked curves; Hilbert scheme Ph. Ellia and M. Fiorentini : Défaut de postulation et singularités du Schéma de Hilbert . Annali Univ. di Ferrara 30 (1984) 185-198. Families, moduli of curves (algebraic), Singularities of curves, local rings, Parametrization (Chow and Hilbert schemes) Défaut de postulation et singularités du schéma de Hilbert
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (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 number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve 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 Brauer group; singular plane elliptic curve; product of symbol algebras Ford, T.: Products of symbol algebras that ramify only on a non-singular plane elliptic curve. Ulam quart. 1, 12 (1992) Galois cohomology, Skew fields, division rings, Brauer groups of schemes Products of symbol algebras that ramify only on a singular plane elliptic curve
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves finiteness of Tate-Shafarevich group; abelian varieties with real multiplication; higher-dimensional elliptic curve; Jacobian of a Shimura curve; Heegner point; Mordell-Weil group Ярощук, В. А., Интегральный инвариант в задаче о качении эллипсоида со специальными распределениями масс по неподвижной поверхности без проскальзывания, Изв. РАН. Мех. тв. тела, 2, 54-57, (1995) Arithmetic ground fields for abelian varieties, Elliptic curves, Totally real fields Finiteness of Ш over totally real 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 algebraic independence; transcendence measures; elimination theory; Weierstrass elliptic function; complex multiplication; semi-resultant of Chow forms W. Dale Brownawell and Robert Tubbs, Large transcendence degree revisited. II. The CM case, Diophantine approximation and transcendence theory (Bonn, 1985) Lecture Notes in Math., vol. 1290, Springer, Berlin, 1987, pp. 175 -- 188. Transcendence (general theory), Elliptic curves, Complex multiplication and abelian varieties Large transcendence degree revisited. II: The CM case
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves category of motives; envelope of schemes; Chow groups; Quillen's \(K\)-theory; homotopy limits; smooth projective varieties; algebraic cycles; hyperenvelope; simplicial schemes; Grothendieck topology; weight complex; canonical triangle; product formula; Gersten complexes of schemes; homotopy equivalence; Tate motive; blow-up; pairings Gillet, H; Soulé, C, Descent, motives and K-theory, Crelle J. Reine Angew. Math., 478, 127-176, (1996) Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Generalizations (algebraic spaces, stacks), \(K\)-theory of schemes, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Grothendieck topologies and Grothendieck topoi Descent, motives and \(K\)-theory
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curve; automorphisms of curves Elliptic curves over global fields, Arithmetic ground fields for curves, Automorphisms of curves Open conditions for infinite multiplicity eigenvalues on elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves control theorems; Shimura-Taniyama-Weil conjecture; elliptic curve; modular curve; deformation rings; Hecke algebras; modular Galois representations; moduli spaces of elliptic curves; modular forms Hida, H.: Geometric modular forms and elliptic curves. World Scientific, Singapore (2000) Galois representations, Elliptic curves over global fields, Research exposition (monographs, survey articles) pertaining to number theory, \(p\)-adic theory, local fields, Holomorphic modular forms of integral weight, Local ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry Geometric modular forms and elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves higher degree Diophantine equations; Galois representations; curves of genus 3 Poonen, B.; Schaefer, F.; Stoll, M., Twists of \(X(7)\) and primitive solutions to \(x^2 + y^3 = z^7\), Duke Math. J., 137, 103-158, (2007) Higher degree equations; Fermat's equation, Abelian varieties of dimension \(> 1\), Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves; family of q-ary optimal locally repairable codes Linear codes (general theory), Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Elliptic curves Optimal locally repairable codes via 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 Dem'yanenko matrix; Hodge group; abelian variety with complex multiplication; class number; order of torsion points; elliptic curves F. Hazama, Demjamenko matrix, class number, and Hodge group.J. Number Theory 34 (1990), 174--177. Cyclotomic extensions, Cyclotomy, Elliptic curves, Iwasawa theory, Complex multiplication and abelian varieties Demjanenko matrix, class number, and Hodge 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 moduli space of curves; noncommutative geometry; Lie algebra cohomology; topological field theory; Batalin-Vilkovisky formalism Families, moduli of curves (analytic), Cohomology of Lie (super)algebras, Infinite-dimensional Lie (super)algebras, Applications of Lie (super)algebras to physics, etc., Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Applications of deformations of analytic structures to the sciences, Topological field theories in quantum mechanics Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press \(\zeta (s)\) and \(L(s, \chi)\), Research exposition (monographs, survey articles) pertaining to number theory, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Distribution of primes An introduction to the theory of the Riemann zeta-function.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Fermat curves; values of \(L\)-functions; CM elliptic curve; regulator; Beilinson conjectures; \(K_ 2\) Ross, R, \(K_{2}\) of Fermat curves and values of \(L\)-functions, C. R. Acad. Sci. Paris Sér., I, 1-5, (1991) Applications of methods of algebraic \(K\)-theory in algebraic geometry, 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) \(K_ 2\) of Fermat curves 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 Elliptic curves; Mordell-Weil rank; Lang's conjecture; rational point; variety of general type Elliptic curves over global fields, Rational points Boundedness of Mordell-Weil ranks of certain elliptic curves and Lang's conjecture.
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves elliptic curves over global fields; arithmetic function fields; sheaves of differentials; Kähler differentials; arithmetic schemes; valuation rings Kunz, E.; Waldi, R.: Integral differentials of elliptic function fields. Abh. math. Sem. univ. Hamburg 74, 243-252 (2004) Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry, Valuation rings Integral differentials of elliptic 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 moduli of curves; Poincaré line bundle; Grassmanian bundle; intersection theory; Chow ring; Gysin morphism; Chern polynomial; Segre classes Special divisors on curves (gonality, Brill-Noether theory), Vector bundles on curves and their moduli, Symmetric functions and generalizations, Combinatorial aspects of representation theory The strong maximal rank conjecture and higher rank Brill-Noether 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 construction of cusp forms of weight 1 and type \(S_ 4\); algorithm due to Birch and Swinnerton-Dyer; Galois representations; octahedral type; 2- coverings of elliptic curves; Artin L-series Bayer P., Math. Z. 207 pp 395-- (1991) Elliptic curves over global fields, Representation-theoretic methods; automorphic representations over local and global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Coverings of curves, fundamental group Galois representations of octahedral type and 2-coverings of elliptic curves
| 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves minimal models; quartic extensions; isomorphism classes of elliptic curves; computer search Special algebraic curves and curves of low genus, Elliptic curves, Software, source code, etc. for problems pertaining to algebraic geometry, Cubic and quartic extensions, Iwasawa theory Elliptic curves with good reduction away from 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 Drinfeld modular curves; motivic cohomology; special values of \(L\)-functions Ramesh Sreekantan, \?\(_{1}\) of products of Drinfeld modular curves and special values of \?-functions, Compos. Math. 146 (2010), no. 4, 886 -- 918. Modular forms associated to Drinfel'd modules, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, 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) \(K_1\) of products of Drinfeld modular curves and special values of \(L\)-functions
| 0 |
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