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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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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The Buzzard–Diamond–Jarvis conjecture for unitary groups
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by Toby Gee, Tong Liu and David Savitt PDF
J. Amer. Math. Soc. 27 (2014), 389-435 Request permission

Abstract:

Let $p>2$ be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod $p$ representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of $(\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.
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Additional Information
  • Toby Gee
  • Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom
  • Email: toby.gee@imperial.ac.uk
  • Tong Liu
  • Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
  • MR Author ID: 638721
  • Email: tongliu@math.purdue.edu
  • David Savitt
  • Affiliation: Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721-0089
  • Email: savitt@math.arizona.edu
  • Received by editor(s): July 5, 2012
  • Received by editor(s) in revised form: May 15, 2013
  • Published electronically: July 3, 2013
  • Additional Notes: The second author was partially supported by NSF grant DMS-0901360.
    The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032.
  • © Copyright 2013 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 27 (2014), 389-435
  • MSC (2010): Primary 11F33, 11F80
  • DOI: https://doi.org/10.1090/S0894-0347-2013-00775-4
  • MathSciNet review: 3164985