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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On the modularity of elliptic curves over $\mathbf{Q}$: Wild $3$-adic exercises


Authors: Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor
Journal: J. Amer. Math. Soc. 14 (2001), 843-939
MSC (2000): Primary 11G05; Secondary 11F80
Published electronically: May 15, 2001
MathSciNet review: 1839918
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Abstract: We complete the proof that every elliptic curve over the rational numbers is modular.


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Additional Information

Christophe Breuil
Affiliation: Département de Mathématiques, CNRS, Université Paris-Sud, 91405 Orsay cedex, France
Email: Christophe.BREUIL@math.u-psud.fr

Brian Conrad
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: bconrad@math.harvard.edu, bdconrad@math.lsa.umich.edu

Fred Diamond
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454
Email: fdiamond@euclid.math.brandeis.edu

Richard Taylor
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: rtaylor@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-01-00370-8
PII: S 0894-0347(01)00370-8
Keywords: Elliptic curve, Galois representation, modularity
Received by editor(s): February 28, 2000
Received by editor(s) in revised form: January 1, 2001
Published electronically: May 15, 2001
Additional Notes: The first author was supported by the CNRS. The second author was partially supported by a grant from the NSF. The third author was partially supported by a grant from the NSF and an AMS Centennial Fellowship, and was working at Rutgers University during much of the research. The fourth author was partially supported by a grant from the NSF and by the Miller Institute for Basic Science.
Article copyright: © Copyright 2001 American Mathematical Society