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Modularity of certain potentially Barsotti-Tate Galois representations

Authors: Brian Conrad, Fred Diamond and Richard Taylor
Journal: J. Amer. Math. Soc. 12 (1999), 521-567
MSC (1991): Primary 11F80; Secondary 11G18
MathSciNet review: 1639612
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Abstract: We show that certain potentially semistable lifts of modular mod$l$ representations are themselves modular. As a result we show that any elliptic curve over the rational numbers with conductor not divisible by 27 is modular.

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Additional Information

Brian Conrad
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Fred Diamond
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854

Richard Taylor

Keywords: Hecke algebra, Galois representation, modular curves.
Received by editor(s): April 1, 1998
Received by editor(s) in revised form: September 1, 1998
Additional Notes: The first author was supported by an N.S.F. Postdoctoral Fellowship, and would like to thank the Institute for Advanced Study for its hospitality. The second author was at M.I.T. during part of the research, and for another part was visiting Université de Paris-Sud supported by the C.N.R.S. The third author was supported by a grant from the N.S.F. All of the authors are grateful to Centre Émile Borel at the Institut Henri Poincaré for its hospitality at the $p$-adic semester.
Article copyright: © Copyright 1999 American Mathematical Society