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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Modularity of certain potentially Barsotti-Tate Galois representations
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by Brian Conrad, Fred Diamond and Richard Taylor PDF
J. Amer. Math. Soc. 12 (1999), 521-567 Request permission

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
  • MR Author ID: 637175
  • Email: bconrad@math.harvard.edu
  • Fred Diamond
  • Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
  • Email: fdiamond@math.rutgers.edu
  • Richard Taylor
  • Email: rtaylor@math.harvard.edu
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 521-567
  • MSC (1991): Primary 11F80; Secondary 11G18
  • DOI: https://doi.org/10.1090/S0894-0347-99-00287-8
  • MathSciNet review: 1639612