publication . Preprint . Article . 2017

Constructing elliptic curves from Galois representations

Andrew Snowden; Jacob Tsimerman;
Open Access English
  • Published: 08 Aug 2017
Abstract
Comment: 9 pages
Subjects
arXiv: Mathematics::Algebraic GeometryMathematics::Number TheoryMathematics::K-Theory and HomologyMathematics::Category Theory
free text keywords: Mathematics - Number Theory, Mathematics - Algebraic Geometry, Algebra and Number Theory, Arithmetic surface, Topology, Galois module, Euler sequence, Elliptic curve, Langlands program, Fontaine–Mazur conjecture, Ideal sheaf, Discrete mathematics, Algebra, Mathematics, Sheaf
Funded by
NSF| CAREER: Combinatorial Categories and Commutative Algebra
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1453893
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Twisted commutative algebras
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1303082
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences

[1] S. Bosch, W. Lu¨tkebohmert, M. Raynaud. N´eron models. Springer-Verlag, Berlin, 1990.

[2] P. Clark. Rational points on Atkin-Lehner quotients of Shimura curves.

[3] V.G. Drinfed. Two-dimensional ℓ-adic representations of the fundamental group of a curve over a finite field and automorphic forms on GL(2). Amer. J. of Math. 105, No. 1 (1983), pp. 85-114

[4] V.G. Drinfeld. Elliptic Modules. II. Math. USSR Sbornik, 31 No .2 (1977).

[5] V.G. Drinfeld. Langland's conjecture for GL(2) over function fields. Proc. ICM (1978).

[6] G. Faltings, G. Wu¨stholz, F. Grunewald, N. Schappacher, U. Stuhler. Rational points. Third edition. Papers from the seminar held at the Max-Planck-Institut fu¨r Mathematik, Bonn/Wuppertal, 1983/1984. With an appendix by Wu¨stholz. Aspects of Mathematics, E6. Friedr. Vieweg & Sohn, Braunschweig, 1992

[7] J.S. Milne. Abelian varieties. http://www.jmilne.org/math/CourseNotes/AV110.pdf

[8] J.-P. Serre. Zeta and L functions, in Arithmetical Algebraic Geometry, Harper and Row, New York, 1965, 82-92.

[9] SGA1: Revˆetements tales et groupe fondamental. S´eminaire de g´eom´etrie alg´ebrique du Bois Marie 1960-61.

[10] G. Shimura. Algebraic number fields and symplectic discontinuous groups. Ann. of Math. (2) 86 (1967), 503-592.

[11] R. Taylor. Remarks on a conjecture of Fontaine and Mazur. J. Inst. Math. Jussieu 1 (2002), no. 1, 125-143.

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publication . Preprint . Article . 2017

Constructing elliptic curves from Galois representations

Andrew Snowden; Jacob Tsimerman;