On the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real number fields
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- by Cristian Virdol
- Proc. Amer. Math. Soc. 137 (2009), 4019-4024
- DOI: https://doi.org/10.1090/S0002-9939-09-10011-4
- Published electronically: July 22, 2009
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References
- Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over $\mathbf Q$: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939. MR 1839918, DOI 10.1090/S0894-0347-01-00370-8
- Noam D. Elkies, Supersingular primes for elliptic curves over real number fields, Compositio Math. 72 (1989), no. 2, 165–172. MR 1030140
- Chandrashekhar Khare, Michael Larsen, and Ravi Ramakrishna, Transcendental $l$-adic Galois representations, Math. Res. Lett. 12 (2005), no. 5-6, 685–699. MR 2189230, DOI 10.4310/MRL.2005.v12.n5.a6
- Hwasin Park and Daeyeoul Kim, Relations among Shafarevich-Tate groups, Honam Math. J. 21 (1999), no. 1, 35–42. MR 1707466
- Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
- B. Mazur, Modular curves and arithmetic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 185–211. MR 804682
- Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380, DOI 10.1007/978-1-4684-9458-7
- Jean-Pierre Serre, Abelian $l$-adic representations and elliptic curves, Research Notes in Mathematics, vol. 7, A K Peters, Ltd., Wellesley, MA, 1998. With the collaboration of Willem Kuyk and John Labute; Revised reprint of the 1968 original. MR 1484415
- C. M. Skinner and Andrew J. Wiles, Nearly ordinary deformations of irreducible residual representations, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), no. 1, 185–215 (English, with English and French summaries). MR 1928993, DOI 10.5802/afst.988
- Richard Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), no. 2, 265–280. MR 1016264, DOI 10.1007/BF01388853
- Richard Taylor, Remarks on a conjecture of Fontaine and Mazur, J. Inst. Math. Jussieu 1 (2002), no. 1, 125–143. MR 1954941, DOI 10.1017/S1474748002000038
- Richard Taylor, Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239. MR 2470688, DOI 10.1007/s10240-008-0015-2
- Cristian Virdol, Zeta functions of twisted modular curves, J. Aust. Math. Soc. 80 (2006), no. 1, 89–103. MR 2212318, DOI 10.1017/S144678870001140X
- Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI 10.2307/2118559
Bibliographic Information
- Cristian Virdol
- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 781239
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2538562