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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. toric varieties; freeness of cohomology groups; McKay correspondence; three-dimensional abelian quotient 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. evaluation of cubic character sums; Legendre symbol; elliptic curves with complex multiplication; Frobenius automorphism; formula for multiplication by \(\sqrt{-3}\) Dimitrios Poulakis, Évaluation d'une somme cubique de caractères, J. Number Theory 27 (1987), no. 1, 41 -- 45 (French).
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. methods of algebraic \(K\)-theory; Hodge theory; algebraic curves; Bloch-Beilinson conjectures; algebraic cycles; Chow groups; monodromy Green, M., Griffiths, P.: The regulator map for a general curve. In: Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000), pp. 117-127, Contemporary Mathematics, vol. 312. American Mathematical Society, Providence (2002)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Kronecker's limit formula; zeta-function of an order; Chowla-Selberg formula; elliptic curves Kaneko, M, A generalization of the chowla-Selberg formula and the zeta functions of quadratic orders, Proc. Jpn. Acad. Ser. A Math. Sci., 66, 201-203, (1990)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Galois representations; elliptic curves; genus-three curves; Prym varieties; Chabauty methods; quadratic \({\mathbb Q}\)-curves Bruin, N.; Fernández, J.; González, J.; Lario, J.-C., Rational points on twists of \(X_0(63)\), Acta Arith., 126, 361-385, (2007)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. \(p\)-adic analogues of the Birch and Swinnerton-Dyer conjecture; Weil elliptic curves; extended Mordell-Weil group; \(p\)-adic height; \(p\)-adic multiplicative period Barry Mazur, John Tate & Jeremy Teitelbaum, ``On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer'', Invent. Math.84 (1986) no. 1, p. 1-48
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. boundedness of the torsion on elliptic curves; Demjanenko matrix
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves; rational points; sequences of consecutive squares M. Kamel and M. Sadek, On sequences of consecutive squares on elliptic curves, Glasnik Mat. 52 (2017), 45--52.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. linear systems of divisor on \(r\)-fold symmetric products of elliptic curves; surfaces of general type; moduli of surfaces; Kodaira-Spencer map; Kuranishi family Catanese, F.; Ciliberto, C., Symmetric products of elliptic curves and surfaces of general type with \(p_g=q=1\), J. Algebr. Geom., 2, 389-411, (1993)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. families of curves; cohomology; infinitesimal Abel-Jacobi mapping; quintic threefold C.H. Clemens , The local geometry of the Abel-Jacobi mapping, in Algebraic Geometry , Bowdoin 1985, Proceedings of Symposia in Pure Mathematics, A.M.S., vol. 46-part 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. abelian subvariety of the Jacobian; symmetric product of curve; double covering of a curve; number of irreducible 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. Hecke operator; weight distribution; binary cyclic codes; families of elliptic curves Schoof, René, Families of curves and weight distributions of codes, Bull. Amer. Math. Soc. (N.S.), 0273-0979, 32, 2, 171-183, (1995)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. crystalline cohomology; representation theory; algebraic groups of Lie type; plane projective curves; Frobenius morphism; filtrations; Weyl modules Haastert, B.; Jantzen, J. C.: Filtrations of the discrete series of \(SL2(q)\) via crystalline cohomology. J. algebra 132, No. 1, 77-103 (1990)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves; group of points; effective addition law
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. double covering of curves; plane curves; elliptic curves Takeshi Harui, Jiryo Komeda, and Akira Ohbuchi, Double coverings between smooth plane curves, Kodai Math. J. 31 (2008), no. 2, 257 -- 262.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. schemes; coherent sheaves; cohomology of schemes; duality theory; algebraic curves; birational geometry of surfaces; arithmetic algebraic curves; arithmetic algebraic surfaces; stable reduction of curves; arithmetic algebraic geometry; birational geometry of algebraic surfaces Qing Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics 6, Oxford University Press, 2002, Translated from the French by Reinie Erné, Oxford Science Publications
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves over function fields; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the Brauer-Siegel theorem
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. recurrence relations; coefficients of the \(n\)-th division polynomial for elliptic curves McKee, J, Computing division polynomials, Math. Comput., 63, 767-771, (1994)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. trigonal curve; ample curves; Prym varieties of two-sheeted coverings
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. torsion zero cycles; Selmer group of the symmetric square; Hyodo-Kato cohomology; selfproduct of a semistable elliptic curve Andreas Langer, Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve, Doc. Math. 2 (1997), 47 -- 59.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Hilbert scheme of points; integral cohomology; Chow motive
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Deligne-Mumford compactification; moduli of curves; stack; mapping class group; orbit category Ebert, J; Giansiracusa, J, On the homotopy type of the Deligne-Mumford compactification, Algebr. Geom. Topol., 8, 2049-2062, (2008)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. cohomology; Witt ring of elliptic curve; symmetric bilinear spaces; algebraic scheme; complete regular curve Arason, Jón Kr.; Elman, Richard; Jacob, Bill: On generators for the Witt ring, Contemp. math. 155, 247-269 (1994)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. multiset; partitions of multiset; elliptic curves; 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. curves of genus two; descent theory; geometric Galois theory; Brumer's family; Humbert's modular equation; Poncelet's pentagon; algebraic correspondences Hashimoto, [Hashimoto 00] K., On Brumer's family of RM-curves of genus two, \textit{Tohoku Math. J. (2)}, 52, 4, 475-488, (2000)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. singular cubics; isogenies; torsion points; elliptic curves over finite fields; elliptic curves over local fields; Selmer groups; duality; rational torsion; heights; complex multiplication; integral points; Galois representations; survey; group law; endomorphism ring; Weil pairing; elliptic functions; formal group; Shafarevich-Tate groups; \(L\)-series; Tate curves; descent; conjecture of Birch and Swinnerton-Dyer Silverman, J. H.: A survey of the arithmetic theory of elliptic curves. Modular forms and Fermat's last theorem (1997)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curve; Heron triangle; specialization; Diophantine triple; family of elliptic curves; 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. orbifolds; elliptic surfaces; coverings of curves; étale fundamental groups; homotopy exact sequences; simply connected Mitsui, K., Homotopy exact sequences and orbifolds, Algebra Number Theory, 9, 1089-1136, (2015)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves over a number field; estimate for the degree of a minimal isogeny F. PELLARIN . Estimation du degré d'une Isogénie entre courbes elliptiques , Comptes Rendus Acad. Sci. de Paris, t. 321, série I, pages 685-688, 1995 , 1995 . MR 97g:11052 | Zbl 0890.11021
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. traces of Hecke operators; modular curves over a finite field; elliptic curves over a finite field; Petersson formula for newforms; Tsfasman-Vlăduţ-Zink theorem
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. algebraic theory of quadratic forms; Witt groups and rings; algebraic \(K\)-theory; algebraic cycles; Chow groups and rings; cohomology operations; motives; projective quadrics Elman, R.; Karpenko, N.; Merkurjev, A., \textit{The Algebraic and Geometric Theory of Quadratic Forms}, 56, (2008), Providence, RI
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. projective embeddings of abelian varieties; Products of elliptic curves Auffarth, R., A note on Galois embeddings of abelian varieties, Manuscr. Math., 154, 279-284, (2017)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves; number fields; torsion group; abelian 2-extensions of \(\mathbb{Q}\); \(K\)-isogeny 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. \(p\)-torsion points of elliptic curves; Galois representations; quadratic number field; semi-stable elliptic curves [13] A. Kraus, \(Courbes elliptiques semi-stables et corps quadratiques\), Journal of Number Theory 60, (1996), 245-253. &MR 14 | &Zbl 0865.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. stable curve; tautological ring; irreducible branched covers; moduli space of smooth \(n\)-pointed curves; Chow ring Tom Graber and Ravi Vakil, On the tautological ring of \overline{\Cal M}_{\?,\?}, Turkish J. Math. 25 (2001), no. 1, 237 -- 243.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. global fields; Drinfeld modules; elliptic curves; distribution of primes; densities
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Chow groups; Milnor \(K\)-theory; Deligne cohomology; infinitesimal deformation; Abel-Jacobi map
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Birch-Swinnerton-Dyer conjecture; mixed motives; motivic cohomology; period conjecture; special values of \(L\)-functions; Deligne's conjecture; Beilinson's conjectures Anthony J. Scholl, Remarks on special values of \?-functions, \?-functions and arithmetic (Durham, 1989) London Math. Soc. Lecture Note Ser., vol. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 373 -- 392.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. locally free resolution of ideals; cohomology groups of ideal sheaf; degree; unirational varieties; degeneracy loci; general bundle morphisms; Hilbert scheme; elliptic normal scrolls Dolores Bazan and Emilia Mezzetti, On the construction of some Buchsbaum varieties and the Hilbert scheme of elliptic scrolls in \Bbb P\(^{5}\), Geom. Dedicata 86 (2001), no. 1-3, 191 -- 204.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Hodge-Deligne theory; cubic hyperresolutions of a k-scheme; singular 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. Chow group; Deligne cohomology James D. Lewis, Regulators of Chow cycles on Calabi-Yau varieties, Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001) Fields Inst. Commun., vol. 38, Amer. Math. Soc., Providence, RI, 2003, pp. 87 -- 117.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. exterior power operations; binary complexes; higher algebraic \(K\)-theory; lambda ring; Dold-Kan correspondence; Dold-Puppe construction; simplicial tensor product; plethysm problem; polynomial functor; Schur algebra; \(K\)-theory of schemes; exterior powers; lambda operations Harris, T., Köck, B., Taelman, L.: Exterior power operations on higher K-groups via binary complexes, preprint, arXiv:1607.01685v2 (2016)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. complex tori; complex abelian varieties; theta functions; theta divisor; elliptic curves; line bundles; moduli spaces of polarized abelian varieties; modular forms; Gauss map Debarre, O., Tores et variétés abéliennes complexes, Cours Spécialisés, vol. 6, (1999), Société Mathématique de France: Société Mathématique de France Paris, EDP Sciences, Les Ulis
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. quadratic form; Witt ring; fundamental ideal; Pfister form; Witt index; higher Witt indices; generic splitting; height of a quadratic form; stable birational equivalence; Chow motif; Tate motif; Rost motif; homogeneous variety; Rost's nilpotence theorem; Steenrod operation; motivic equivalence Kahn, B., \textit{formes quadratiques et cycles algébriques [d'après rost, Voevodsky, vishik, karpenko ...], exposé bourbaki no. 941}, Astérisque, 307, 113-163, (2006)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. algebraic geometry; uniformly bounded p-torsion of elliptic curves; order of group of p-torsion points Manin, Ju. I., The \textit{p}-torsion of elliptic curves is uniformly bounded, Izv. Akad. Nauk SSSR Ser. Mat., 33, 459-465, (1969)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. nef cone; pseudoeffective cone; semistability; cone of curves; fibre product of projective bundle over a 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. algebraic cycle; additive higher Chow group; Witt vectors; de Rham-Witt complex A. Krishna and J. Park, \textsl{On additive higher Chow groups of affine schemes}, Doc. Math. \textbf{21}, (2016), 49--89. https://www.elibm.org/article/10000430; zbl 1357.14014; MR3465108
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. descent on elliptic curves; invariants of binary quartics; group of rational points; elliptic curve; algorithm; Mordell-Weil group --------, Classical invariants and \(2\)-descent on elliptic curves , J. Symbolic Comput., 31 (2001), 71-87.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. singular point of symmetric product of curve; Abel-Jacobi map; osculating cones; hyperelliptic curves; trigonal curves F. Bardelli and L. Verdi , Un'osservazione sul teorema di singolarità di Riemann-Kempf per curve iperellittiche e trigonali , Boll. Un. Mat. It. (6) 5-A (1986) 201-204.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. \(K3\) surface; Hilbert scheme of points; integral cohomology; cup product 8. S. Kapfer, Computing cup-products in integral cohomology of Hilbert schemes of points on K3 surfaces, to appear in LMS J. Comput. Math.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. torsion of elliptic curves
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Klein curves; hyperbolic planes; Riemann surfaces; triangle groups; Hurwitz curves; elliptic functions; moduli of elliptic integrals; geometric aspects of \(\text{PSL}(2\mathbb{Z}/7\mathbb{Z})\)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Prym varieties; coverings of stable plane curves; complete intersections of three quadrics; Torelli theorem Debarre, O, Le théorème de Torelli pour LES intersections de trois quadriques, Invent. Math., 95, 507-528, (1989)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves over a local field; algorithm for the reduction type of a minimal model; characteristic 2; characteristic 3; Weierstrass model; 315 Papadopoulos, Ioannis, Sur la classification de Néron des courbes elliptiques en caractéristique résiduelle \(2\) et \(3\), J. Number Theory, 44, 2, 119-152, (1993)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. rank of elliptic curves; average function Stéfane Fermigier, Une courbe elliptique définie sur \? de rang \ge 22, Acta Arith. 82 (1997), no. 4, 359 -- 363 (French).
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. zeta functions of groups; finitely generated nilpotent groups; Grothendieck rings; elliptic curves; arithmetic of nilpotent groups M. du Sautoy, ''Counting subgroups in nilpotent groups and points on elliptic curves,'' J. Reine Angew. Math., vol. 549, pp. 1-21, 2002.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. number of sections of twists of vector bundle; moduli space of all rank two stable vector bundles; nearly natural cohomology; minimal model; number of irreducible components; Albanese varieties
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Brauer groups; indecomposable division algebras; noncrossed products; ramification; function fields of smooth curves; non-crossed product central division algebras; exponents; indices; periods; tensor products of central algebras E. Brussel, K. McKinnie, and E. Tengan, Indecomposable and noncrossed product division algebras over function fields of smooth \?-adic curves, Adv. Math. 226 (2011), no. 5, 4316 -- 4337.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. supersingular elliptic curves; Diffie-Hellman cryptosystems; multiplication of points on elliptic curves; public key cryptosystems
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Leech lattice; Mordell-Weil lattice; elliptic curves; function field of a hyperelliptic curve; minimal vectors N. D. Elkies, ''Mordell-Weil lattices in characteristic 2, II: The Leech lattice as a Mordell-Weil lattice,'' Invent. Math., vol. 128, iss. 1, pp. 1-8, 1997.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. algebraic groups; irreducible representations; Hopf algebras; Lie algebras; unipotent algebraic groups; tensor product; semisimple group representations; varieties; dimension theory of local rings; tangent spaces; Borel subgroups; Galois cohomology; automorphism groups; weights; universal enveloping algebra Hochschild, G.P.: Basic theory of algebraic groups and Lie algebras. Graduate Texts Math. \textbf{75}, (1981)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. minimal free resolution of homogeneous coordinate ring; elliptic ruled surface; very ample line bundle; adjoint bundle; Koszul cohomology; cohomology vanishings Gallego, F.J.; Purnaprajna, B.P., Higher syzygies of elliptic ruled surfaces, J. Algebra, 186, 626-659, (1996)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. projective geometry; elliptic functions; Differential geometry; Analytical geometry; Correspondence principle; Singularities; Curves; Surfaces; Abelian Functions; History of Mathematics; Algebraic Geometry; Functions of a Complex Variable Enriques, F., Chisini O.: Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche. 1. Vol. I, II, volume 5 of Collana di Matematica [Mathematics Collection]. Nicola Zanichelli Editore S.p.A., Bologna. Reprint of the 1924 and 1934 editions (1985)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. \(l\)-adic representation; theta series; \(l\)-adic cohomology of Siegel three-folds; automorphic representations; modular forms; theta correspondence; holomorphic Siegel modular form; theta lifting Harris, M.; Soudry, D.; Taylor, R., \textit{\(\mathcal{l}\)}-Adic representations associated to modular forms over imaginary quadratic fields I. Lifting to \(\operatorname{GSp}_4(\mathbb{Q})\), Invent. Math., 112, 377-411, (1993)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic fibrations; models of curves; Shafarevich pairing; abelian varieties; Picard functor; pro-algebraic groups Bertapelle, A.; Tong, J., On torsors under elliptic curves and serre's pro-algebraic structures, Math. Z., 277, 91-147, (2014)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Shafarevich-Tate group of elliptic curves [9]J. E. Cremona and B. Mazur, Visualizing elements in the Shafarevich--Tate group, Experiment. Math. 9 (2000), 13--28.
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curves; logarithmic derivative; Picard group; first cohomology group Coombes, K. R.: Elliptic curves and logarithmic derivatives. Journal of pure and applied algebra 138, 21-38 (1999)
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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. algebraic fundamental group; moduli space of curves; Galois group; Abel-Jacobi map; algebraic cycle; non-abelian Galois representation; mapping class group Hain, R.; Matsumoto, M., Galois actions on fundamental groups of curves and the cycle \(C-C^-\), J. Inst. Math. Jussieu, 4, 363-403, (2005)
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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. irreducible hypersurfaces; projective space; Galois field; classification of curves of higher degree; classification of hypersurfaces; geometric properties Tallini, G., Sulle ipersuperfici irriducibili d'ordine minimo che contengono tutti i punti di uno spazio di Galois \(S_{r, q}\), Rend. Mat. Appl. (5), 20, 431-479, (1961)
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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. algebraic cycle; abelian variety; Chow ring; symmetric product; Jacobian
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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. elementary category; complete categories; cocomplete categories; homology theory for the category of cosheaves; generating family of projective objects; injectives; abelian category; tensor product; hom-functors; hyperhomology for cosheaves; homology of cosheaves; cohomology of sheaves; taut spaces; Kronecker product; cap-product; singular homology J.-P. Schneiders, Cosheaves homology , Bull. Soc. Math. Belg. Sér. B 39 (1987), 1--31.
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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. moduli space of curves; cohomology; tautological groups
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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. enveloping algebra of the Heisenberg Lie algebra; standard algebras with 2 or 3 generators; effective criterion to decide whether a given standard algebra of dimension 3 is regular; automorphisms of elliptic curves Artin, M., Tate, J., Van den Bergh, M.: Some Algebras Associated to automorphisms of Elliptic Curves, The Grothendieck Festschrift, vol. 1, Progress in Mathematics, vol. 86, pp. 33-85. Brikhäuser, Basel (1990)
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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. Cartier-Dieudonné theory; sheaf of K-groups; augmented artinian local k-algebras; crystalline cohomology; formal Picard group; Artin-Mazur groups; Witt vector cohomology; Chow group Stienstra, J.: Cartier-Dieudonné theory for Chow groups. J. Reine Angew. Math. \textbf{355}, 1-66 (1985) (correction. J. Reine Angew. Math. \textbf{362}, 218-220 (1985))
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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. unramified cohomology; 0-cycle; universal triviality of \(\mathrm {CH}_0\); complex surfaces; cubic fourfold; quadric fibration; Clifford algebra
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Wronskian correspondence; coarse moduli space of curves; cycle class; canonical divisor
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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. abelian functions; elliptic functions; Jacobians; hyperelliptic curves; hyperelliptic functions; Lie algebra of derivations; polynomial vector 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. number of rational points; modular curve; number of points of given degree; number of elliptic curves with rational isogeny Frey, G., \textit{curves with infinitely many points of finite degree}, Israel J. Math., 85, 79-83, (1994)
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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. quiver variety; stable envelope; elliptic cohomology; Hilbert scheme of points in the plane
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Mordell-Weil groups; division of points on abelian varieties with complex multiplication; L-function; triviality of the Galois module structure; elliptic curves M. J. Taylor, Mordell-Weil groups and the Galois module structure of rings of integers. Illinois J. Math. 32 (1988), 428-452. Zbl0631.14033 MR947037
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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. elliptic curves; point multiplication; characteristic three Smart N.P., Westwood E.J. (2003). Point multiplication on ordinary elliptic curves over fields of characteristic three. Appl Algebra Eng Comm Comput 13(6):485--497
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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. stratification of moduli space; moduli space of smooth non-hyperelliptic genus three curves; Del Pezzo surfaces; Poincaré polynomials Looijenga E.: Cohomology of \({\mathcal{M}}_3\) and \({\mathcal{M}}_3^1\). In: Bödigheimer, C.-F., Hain, R.M. (eds.) Mapping Class Groups and Moduli Spaces of Riemann Surfaces, volume 150 of Contemporary Mathematics, pp. 205-228 (1993)
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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. very ample invertible sheaf on a curve of genus three; Noether-Enriques- Petri theorem; intersection of quadrics; curves of genus three embedded by complete linear 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. integrable differential equations; coverings of elliptic curves; Landau- Lifshitz equation; algebraical approach; Bäcklund-Darboux transformation I. V. Cherednik, Math. USSR-Izv., 22, 357--377 (1984).
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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. number of integral points; rank of the group of rational points on an elliptic curve; rational points on the Jacobian variety; lower bound for the canonical height on elliptic curves; twisted Catalan curves ----,A quantitative version of Siegel's theorem, J. reine ang. Math.378 (1987), 60--100
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Selmer group of twists of elliptic curves; \(\mathbb Q\)-rational torsion point; \(p\)-class group Frey G.: On the Selmer group of twists of elliptic curves with \({\mathbb{Q}}\) -rational torsion points. Can. J. Math. 40, 649--665 (1988)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Calabi-Yau 3-folds; Schoen 3-folds; fiber product of relatively minimal rational elliptic surfaces with section; nonsimply connected Calabi-Yau 3-folds; group actionss; automorphisms 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. elliptic curves; ranks of elliptic curves; Selmer groups; Cramer model; probabilistic model
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. infinite symmetric products; hypercube conjecture; Fourier transform; Chow homology; Chow rings; Chow cohomology; eigenvalues of an abelian variety Kimura, S.; Vistoli, A., Chow rings of infinite symmetric products, Duke Math. J., 85, 411-430, (1996)
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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. Bogomolov-Miyaoka-Yau inequality; arithmetic surfaces; effective bounds on the heights of rational points; bounding the minimal discriminant of an elliptic curve; Fermat curves; elliptic fibrations
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. genus \(\neq 1\); hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; families of curves
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Proceedings; Colloquium; Washington, DC (USA); National Academy of Sciences; Elliptic curves; Modular forms
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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. moduli spaces of higher dimensional varieties; del Pezzo surfaces; elliptic 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. surfaces of general type; fundamental group of surfaces; quotients of products of curves; product-quotient surfaces Bauer, I.; Catanese, F.; Grunewald, F.; Pignatelli, R., Quotients of products of curves, new surfaces with \(p_g = 0\) and their fundamental groups, Amer. J. Math., 134, 4, 993-1049, (2012)
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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. 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.
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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. Manin constant; Stickelberger element; modular parametrizations of elliptic curves
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. 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)
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. étale cohomology; algebraic cycles; motivic cohomology; higher Chow groups
0
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. 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.
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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. 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
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