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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 curves; topology of moduli spaces; cohomology rings; Hodge structures; discriminantal varieties; Borel-Moore cohomology' rational cohomology; moduli of curves; discriminants Tommasi O. (2005). Rational cohomology of the moduli space of genus 4 curves. Compos. Math. 141(2): 359--384 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 of curves; metric ribbon graphs; Penner's matrix model; recursion of Eynard-Orantin type; Grothendieck's dessins d'enfants; Deligne-Mumford stack; psi-classes; Virasoro constraint M. Mulase and M. Penkava, \textit{Combinatorial Structure of the Moduli Space of Riemann Surfaces and the KP Equation}, unpublished [http://www.math.ucdavis.edu/~mulase/texfiles/1997moduli.pdf]. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. fibration method; elliptic curves; computation of \(L\)-functions of hyperelliptic curves over the rational function field | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. intersection of two plane curves; deformation of singularities; linear system; degeneration; limit 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. crystalline cohomology of higher level; Poincaré lemma; PD structure of higher level Miyatani, K.: Finiteness of crystalline cohomology of higher level. Ann. inst. Fourier 65, No. 3, 975-1004 (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. Diophantine theory of genus 1 curves; local-global principle; rational points; heights; finite basis theorem; Tate-Shafarevich group; arithmetic of elliptic curves J.W.S. Cassels, \textit{Lectures on elliptic curves}, \textit{Lond. Math. Soc. Stud. Texts}\textbf{24}, Cambridge University Press, Cambridge, U.K., (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. abelian sheaves; higher dimensional generalizations of elliptic sheaves; moduli spaces of abelian sheaves; algebraic stacks Urs Hartl , Uniformizing the Stacks of Abelian Sheaves , Number fields and function fields - two parallel worlds, Progress in Mathematics 239, Birkhäuser, 2005, p. 167-222 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 stability; Chow weight; geometric invariant theory; Hilbert-Mumford criterion; moduli 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. Birch Swinnerton-Dyer conjecture; elliptic curves; height of the Heegner points; derivative of the L-series; class number 3 problem D. Zagier, ''\(L\)-series of elliptic curves, the Birch-Swinnerton-Dyer conjecture, and the class number problem of Gauss,'' Notices Amer. Math. Soc., vol. 31, iss. 7, pp. 739-743, 1984. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. rational map; rank of Mordell-Weil group; rational points; family of elliptic curves; cyclic cubic point | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Auslander-Reiten quiver; germ of a normal complex surface singularity; isomorphism classes of vector bundles; reflexive modules; reduction cycle; rational singularities; minimal-elliptic singularities; simply- elliptic singularites; torsion free modules over plane curve singularities Kahn, Reflexive Moduln auf einfach-elliptischen Flächensingularitäten, Dissertation (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. division algebras; reduced norms; function field of \(p\)-adic curves; Galois 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. decomposition of uniform fiber bundles over Grassmannian; cohomology ring of flag variety; Chow ring Guyot M.: Caractérisation par l'uniformité des fibrés universels sur la Grassmannienne. Math. Ann. 270, 47--62 (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. fast algorithm; counting points on elliptic curves; finite fields of small characteristic | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. algorithmic number theory; zeta functions; elliptic curves; modular forms; \(p\)-adic cohomology Antoine Chambert-Loir, Compter (rapidement) le nombre de solutions d'équations dans les corps finis, Astérisque 317 (2008), Exp. No. 968, vii, 39 -- 90 (French, with French summary). Séminaire Bourbaki. Vol. 2006/2007. | 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. rational curves; quantum cohomology ring; operads; stable trees; Gromov-Witten invariants; Frobenius manifold; WDVV equation; Künneth formula; intersection theory of the moduli space; stable genus-0 curves with \(n\) marked points Kaufmann, R, The intersection form in \(H^### ({\overline{M}}_{0, n})\) and the explicit Künneth formula in quantum cohomology, Int. Math. Res. Not., 19, 929-952, (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. Mordell-Weil rank of elliptic curves Ono, T.: Tringles and Elliptic Curves. II. ibid., 70A, 223-225 (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. Calabi-Yau manifolds; Maple; mirror symmetry; quantum cohomology; number of rational curves; Calabi-Yau hypersurfaces S. Katz, Rational curves on Calabi-Yau manifolds: Verifying predictions of Mirror Symmetry, Algebraic Geometry , Marcel-Dekker, New York, 1994. CMP 95:04 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 stack of marked curves; global deformations of Lie algebras; Pursell-Shanks theory; Lie algebra 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. moduli of curves; Chow stability | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. distribution of the numbers of points on elliptic curves over a finite prime field J. F. McKee, Subtleties in the distribution of the numbers of points on elliptic curves over a finite prime field, J. London Math. Soc., to appear. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. rational curves; stable algebraic curves; quantum cohomology of a complex projective algebraic manifold; cohomological field theory; variation of Hodge structures; mirror dual manifold; Gromov-Witten classes; operads for moduli spaces of stable curves M. Kontsevich and Y. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), no. 3, 525-562. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. integral Chow ring, moduli stack of curves, plane quartics | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. restricted tangent bundle; cohomology of restricted tangent bundle; symmetric product of tangent bundle | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Jacobi sum; special values of L-function; Hecke character; Abelian number field; periods 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. \(K3\)-surface; Prym curves; linear systems; contact curves of two Kummer surfaces; Horrocks-Mumford bundle | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Chow groups; elliptic curves; \(K\)-theory sheaf Michael Spiess, On indecomposable elements of \?\(_{1}\) of a product of elliptic curves, \?-Theory 17 (1999), no. 4, 363 -- 383. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. KdV equation; integrable Hamiltonian systems; Riemann surfaces; elliptic functions; theta functions; coverings of curves A. O. Smirnov, ''Finite-gap elliptic solutions of the KdV equation,'' Acta Appl. Math., 36 (1994), 125--166. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Fiber product of elliptic surfaces; Geometric 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. arithmetic curves; line bundles with metrics; Arakelov class group; compactified Chow group; compactified Picard group; Arakelov theory; finiteness of the Picard groups; Arakelov ray class 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. determination of an \(L\)-function from one value; elliptic curves in Weierstrass normal form; modular elliptic curve; isogeny; transcendence theory Stark, H.M.: On the determination of an \(L\)-function from one value. In: Analytic Number Theory, vol. 2 (Allerton Park, IL, 1995). Progress in Mathematics, vol. 139, pp. 737-743. Birkhäuser Boston, Boston (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. quadratic forms; function field of a quadric; spinor norm; Galois cohomology; unramified cohomology; étale cohomology; Chow group; spectral sequence B. Kahn and R. Sujatha, Unramified cohomology of quadrics II, Duke Mathematical Journal 106 (2001), 449--484. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. finite automorphism group; elliptic fibrations; Enriques surfaces; universal covering surface; global Torelli theorem; dual graphs of nodal curves Kondō, S., Enriques surfaces with finite automorphism groups, Jpn. J. Math., 12, 191-282, (1986) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. tropicalization; moduli of curves; Berkovich spaces; skeletons; toroidal 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. double coverings of genus 1; local non-dyadic field; monic polynomial; index; 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. cohomology group; cuspidal representation; dimension formula; automorphic forms; elliptic curves; good reduction; Lefschetz fixed point theorem; imaginary quadratic fields Krämer, N.: Beiträge zur arithmetik imaginärquadratischer zahlkörper. Bonner math. Schriften 161 (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. Weierstrass points; curves of low genus; double covering; elliptic involution Keem, C; Martens, G, On curves with all Weierstrass points of maximal weight, Arch. Math., 94, 339-349, (2010) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 three; real multiplications; abelian variety | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Euler spiral; Weierstrass curve; Bézier curves; rectangular hyperbola; quadratrix of Hippias; space filling curves; curves of constant width; normal curve; Catenary; elliptic curves; envelopes; arch; simple pendulum; Fibonacci's method; Greek problems | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. homological mirror symmetry; hypersurface; Landau-Ginzburg model; wrapped Fukaya category; wrapped Floer cohomology; derived category of coherent sheaves; higher-dimensional pants | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. finiteness of second Chow group; singular surfaces; étale cohomology 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. Transformations of elliptic functions; 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. automorphic forms; toroidal automorphic forms; elliptic curves; vector bundles; graphs of Hecke operators Lorscheid, O., Automorphic forms for elliptic function fields, Math. Z., 272, 3-4, 885-911, (2012) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 schemes of elliptic curves; Hecke algebra; rank of the group of integral modular units; congruence subgroup Scholl, A. J., On modular units, Math. Ann., 285, 3, 503-510, (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. postulation; curves of maximal rank in projective 3-space; hyperplane bundle; linearly normal elliptic curve E. Ballico -Ph. Ellia,Sur la postulation des courbes de P 3 et de leur projections, C. R. Acad. Sc. Paris,299 (1984), pp. 237--240. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 polylogarithm; arithmetic Chow groups; Arakelov geometry; Deligne cohomology | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. linear sieve with weights; group order of elliptic curves Steuding, Jörn; Weng, Annegret, On the number of prime divisors of the order of elliptic curves modulo \textit{p}, Acta arith., 117, 4, 341-352, (2005) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. motivic cohomology; higher Chow group; Hodge theory Lewis J.\ D., A note on indecomposable motivic cohomology classes, J. reine angew. Math. 485 (1997), 161-172. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 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. modular \(j\)-invariant; homotopy Lie theory; period integrals of elliptic curves; differential graded Lie 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. elliptic curves; isogenies; isolated curves; embedding degree; cryptography; distribution of primes | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curve; Witt ring over elliptic curve; étale cohomology of a curve Arason J. Elman R. Jacob B. On the Witt ring of an elliptic curve (in preparation) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. modular elliptic curve; twisted self-fiber product; modular (new) forms of weight 4 Schütt, M., On the modularity of three Calabi-Yau threefolds with bad reduction at 11 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. elliptic curve over the rational function field; ring of invariants; excellent families of elliptic curves; Weyl group; Mordell-Weil lattice of a rational elliptic surface Shioda, T; Usui, H, Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli, 41, 169-217, (1992) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. average period of an elliptic curve; 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. valuations of division polynomials; elliptic curves Cheon, J., Hahn, S.: Explicit valuations of division polynomials of an elliptic curve. Manuscripta Math. 97, 319--328 (1998) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; rational equivalence class; Hilbert scheme of space curves Gotzmann, G. 1994.Der kombinatorische Teil der ersten Chowgruppe eines Hilbertschemas von Raumkurven, Schriftenreihe des Mathematischen Instituts der Universität Münster, 3. Serie 13 98Münster: Universität Münster, Mathematisches Institut. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 theorems; application to rational curves; entire functions; numbers; determinant; product of differences; roots; equation of \(m^{\text th}\) degree; forms; analytic representation; theory of involutions | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 higher genus; JFM 56.0180.05; finiteness of integral points on curves; Gelfond-Baker method; effective version of Siegel's theorem; Galois 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. tachyon scattering amplitudes; divisiors with complex coefficients; moduli space of complex algebraic curves of genus \(g\) with \(n\) given points; Belavin-Knizhnik theorem; bosonic string theory; Polyakov volume form; Weil-Deligne pairings; Arakelov measures; Quillen metrics | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. efficiency of function field sieve; discrete logarithms in finite fields; supersingular elliptic curves Granger, R., Holt, A., Page, D., Smart, N.P., Vercauteren, F.: Function field sieve in Characteristic three.In: Algorithmic Number Theory Symposium - ANTS VI, pp. 223--234. Springer LNCS 3076 (2004) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; partitions of a set; Mordell equations; Lutz-Nagell 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. Hodge cohomology groups; infinite dimensionality of the Chow group V. Srinivas, Gysin maps and cycle classes in Hodge cohomology, Proc. Indian Acad. Sci. Math. Sci. 103 (1993), 209--247. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. sine-Gordon equation; Lamb ansatz; three-sheeted covering; elliptic finite-gap solutions; Krichever curve; two-gap Lamé potential; doubly periodic solutions A. O. Smirnov. ''3-Elliptic solutions of the sine-Gordon equation, Mat. Zametki, 62, No. 3, 440--452 (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 curves over finite fields; complex multiplication; construction of elliptic curves over finite fields; subgroup of large prime order | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 of stable marked rational curves; enumerative geometry; Gromov-Witten invariants; quantum cohomology; stable maps Joachim Kock and Israel Vainsencher, A fórmula de Kontsevich para curvas racionais planas, 22^{\?} Colóquio Brasileiro de Matemática. [22nd Brazilian Mathematics Colloquium], Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 1999 (Portuguese). | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 bundles; mod two cohomology; skew Schur polynomial; cup product pairings | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. isolated curve singularities; zero-dimensional schemes; unstable rank-two vector bundles; equisingular families of curves; prescribed singularities Keilen T., Trans. Amer. Math. Soc. 355 pp 3485-- (2003) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. normal basis; optimal normal bases; elliptic curves over finite fields; elliptic curve cryptosystems; codes; finite fields; finite field arithmetic; factoring of polynomials; discrete logarithm problem; irreducible polynomials; survey Menezes, A. J., Blake, I. F., Gao, X., Mullin, R. C., Vanstone, S. A., \& Yaghoobian, T. (1993). Applications of finite fields. Kluwer international series in engineering and computer science. ISBN: 0-7923-9282-5. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. surfaces isogenous to a product of curves; finite groups; mapping class groups; moduli spaces; surfaces of general type Penegini, M.: Surfaces isogenous to a product of curves, braid groups and mapping class groups. In: Beauville Surfaces and Groups, Springer Proceedings in Math. and Stats. pp. 129-148 (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. Birch-Swinnerton-Dyer conjecture; Families of elliptic curves with large Tate-Shafarevich groups; Selmer group Kramer, K., A family of semistable elliptic curves with large Tate-Shafarevich groups, Proc. Amer. Math. Soc., 89, 379-386, (1983) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. quantum cohomology; Frobenius manifolds; isomonodromic deformations of connections; versal deformations; Calabi-Yau manifolds; algebraic stacks; homological Chow groups; Gromov-Witten-type invariants; Painlevé VI Yu. I. Manin, \textit{Frobenius manifolds, Quantum Cohomology, and Moduli Spaces} (Faktorial, Moscow, 2002) [in Russian]. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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-forms; elliptic quartic curves; Plücker coordinates | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 curves; relations with integrable systems; coverings of curves; soliton equations; finite-gap potentials; elliptic functions Treibich, A.: Beyond the exceptional covers and their canonical hyper-elliptic potentials preprint 99-3. 43 (1999) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. \(KV\) groups; higher \(K\)-theory; Karoubi-Villamayor theory; higher Chow construction; spectral sequences; motivic cohomology Landsburg S. , Some filtrations on higher K-theory and related invariants , K-theory 6 ( 1992 ) 431 - 457 . MR 1194843 | Zbl 0774.14006 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. rational curves; number of rational points; elliptic surface Billard, H.: Sur la répartition des points rationnels de surfaces elliptiques, J. reine angew. Math. 505, 45-71 (1998) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. sums of two cubes; Heegner points; elliptic curve; prime numbers | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; Heron triangles A. Dujella and J. Peral, Elliptic curves coming from Heron triangles, Rocky Mountain J. Math. 44 (2014), 1145--1160. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; positive characteristic; ring of unipotent bundles; tensor product of matrices; modular representation ring | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. compactifications of families of elliptic curves; threefolds with trivial canonical bundle; Calabi-Yau threefolds A. I. Markushevich,Theory of Functions of a Complex Variable, Chelsea, New York, 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. Weil-Deligne group; non-archimedean local field; \(L\)-factor; conductor; \(\varepsilon\)-factor; root number; elliptic curves Rohrlich, D. E., \textit{elliptic curves and the Weil-Deligne group}, Elliptic curves and related topics, 125-157, (1994), American Mathematical Society, 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. 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. (1988). An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Studies in Advanced Mathematics 14 . Cambridge: Cambridge Univ. Press. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 variety; toric bundle; complete fan of cones; cohomology; total Chern classes; Chow ring; Grothendieck ring Michałek, M., Miró-Roig, R.M.: Smooth monomial Togliatti systems of cubics. Available at arXiv:1310.2529 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; torsors; curves of genus one; models; degenerations; dual graphs; rational points | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. \(K3\) surfaces; elliptic curves; field of moduli; complex multiplication; class field theory; abelian 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. tachyon scattering amplitudes; divisors with complex coefficients; moduli space of complex; algebraic curves of genus g with n given points; Belavin-Knizhnik theorem; bosonic string theory; Polyakov volume form; Weil-Deligne pairings; Arakelov measures; Quillen metrics Voronov, AA, A unified approach to string scattering amplitudes, Commun. Math. Phys., 131, 179, (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. Chow groups with coefficients; complexes of cycles; localization complexes for varieties; cycle modules; intersections; Chow groups M.~Rost, \emph{Chow groups with coefficients}, Doc. Math. 1 (1996), No. 16, 319--393. https://www.elibm.org/article/10000028; zbl 0864.14002; MR1418952 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. endomorphism ring; real algebraic structure of complex elliptic curves as real algebraic surfaces; complex multiplication; real algebraic torus J. Huisman, The underlying real algebraic structure of complex elliptic curves. Math. Ann.294 (1992), 19-35 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; components of the moduli space; fibration by genus two curves; universal deformation; Euler number W. K. Seiler, Moduli of surfaces of general type with a fibration by genus two curves. Math. Ann.301, 771--812 (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. Chow quotient; Hilbert quotient; moduli of curves; phylogenetic trees; geometric invariant theory; toric geometry; tropical geometry Gibney, A., Maclagan, D.: Equations for Chow and Hilbert quotients. Algebra Number Theory. \textbf{7}, 855-885 (2010). arXiv:0707.1801 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. theta-characteristics; family of smooth projective curves; characteristic two | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Bibliography; moduli spaces of algebraic curves; Hilbert schemes; stable algebraic curves; Deligne-Mumford compactification; Brill-Noether theory; geometric invariant theory; families of curves J. Harris, I. Morrison, \textit{Moduli of curves}. Springer 1998. | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Hopf construction; points of infinite order; elliptic curves; torsion point | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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; double ramification cycle; quantum KdV; quantum tau function; Hurwitz numbers | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. Gromov-Witten invariants, quantum cohomology, moduli space of curves, tautological ring X Liu, Gromov-Witten invariants and moduli spaces of curves, Eur. Math. Soc., Zürich (2006) 791 | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. smooth Deligne cohomology; transgression; higher parallel transport; higher holonomy Y. Terashima, Higher-dimensional parallel transports for Deligne cocycles, in: M. Guest, et al. (Eds.), Integrable Systems, Topology and Physics, Contemporary Math. Vol. 309, A.M.S., 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. generation of binary sequences; trace functions; elliptic curves; elliptic curve pseudorandom sequences; EC-sequences; elliptic curve public-key cryptosystems Gong, G.; Berson, T. A.; Stinson, D. R., Elliptic curve pseudorandom sequence generators, \textit{Selected Areas in Cryptography}, Lecture Notes in Computer Science, 1758, 34-48, (2000), Springer, Berlin, Germany | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 stacks; Moduli of hyperelliptic curves; Picard 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. elliptic curves over finite fields; bilinear complexity; finite field extension; complexity of bilinear multiplication; Chudnovsky algorithm; existence; optimal multiplication algorithm Shokrollahi, M. A.: Optimal algorithms for multiplication in certain finite fields using elliptic curves. Research Report, Universität Bonn; submitted for publication | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; 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 group of Chow group; codimension two cycles; rational equivalence; modulo rational equivalence Jean-Louis Colliot-Thélène and Wayne Raskind, Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion, Invent. Math. 105 (1991), no. 2, 221 -- 245 (French, with English summary). | 0 |
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