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On the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real number fields


Author: Cristian Virdol
Journal: Proc. Amer. Math. Soc. 137 (2009), 4019-4024
MSC (2000): Primary 11F03, 11F80, 11R37, 11R42, 11R56, 11R80
DOI: https://doi.org/10.1090/S0002-9939-09-10011-4
Published electronically: July 22, 2009
MathSciNet review: 2538562
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  • [BCDT] C. Breuil, B. Conrad, F. Diamond, R. Taylor, On the modularity of elliptic curves over $ \mathbb{Q}$: Wild $ 3$-adic exercises, J. Amer. Math. Soc. 14 (2001), 843-939. MR 1839918 (2002d:11058)
  • [E] N.D. Elkies, Supersingular primes for elliptic curves over real number fields, Compositio Math. 72, no. 2 (1989), 165-172. MR 1030140 (90i:11058)
  • [KLR] C. Khare, M. Larsen, R. Ramakrishna, Transcendental $ l$-adic Galois representations, Math. Res. Lett. 12 (2005), no. 5-6, 685-699. MR 2189230 (2006m:11078)
  • [KP] D. Kim, H. Park, Relations among Shafarevich-Tate groups, Honam Math. J. 21 (1999), no. 1, 35-42. MR 1707466 (2000j:11086)
  • [L] R.P. Langlands, Base change for GL$ _{2}$, Ann. of Math. Studies, 96, Princeton University Press, University of Tokyo Press, 1980. MR 574808 (82a:10032)
  • [M] B. Mazur, Modular curves and arithmetic, Proceedings of International Congress of Mathematicians (Warsaw, 1983), PWN, Warsaw, 1984, 185-211. MR 804682 (87a:11054)
  • [S] J-P. Serre, Linear representations of finite groups, Springer-Verlag, 1977. MR 0450380 (56:8675)
  • [S1] J-P. Serre, Abelian $ l$-adic representations and elliptic curves. Revised preprint of the 1968 edition, A K Peters, Ltd., Wellesley, MA, 1998. MR 1484415 (98g:11066)
  • [SW] C. Skinner, A. Wiles, Nearly ordinary deformations of irreducible residual representations, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), no. 1, 185-215. MR 1928993 (2004b:11073)
  • [T] R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), 265-280. MR 1016264 (90m:11176)
  • [T1] R. Taylor, Remarks on a conjecture of Fontaine and Mazur, Journal of the Institute of Mathematics of Jussieu 1 (2002), 125-143. MR 1954941 (2004c:11082)
  • [T2] R. Taylor, Automorphy for some $ l$-adic lifts of automorphic mod $ l$ representations. II, Publ. Math. IHES 108 (2008), 183-239. MR 2470688
  • [V] C. Virdol, Zeta functions of twisted modular curves, J. Aust. Math. Soc. 80 (2006), 89-103. MR 2212318 (2006k:11114)
  • [W] A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), 443-551. MR 1333035 (96d:11071)

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Additional Information

Cristian Virdol
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

DOI: https://doi.org/10.1090/S0002-9939-09-10011-4
Received by editor(s): March 9, 2009
Received by editor(s) in revised form: April 7, 2009
Published electronically: July 22, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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