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
DOI:
https://doi.org/10.1090/S0894-0347-01-00370-8
Published electronically:
May 15, 2001
MathSciNet review:
1839918
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Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
615110
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
MR Author ID:
637175
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
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
