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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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Even Galois representations and the Fontaine–Mazur conjecture. II
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by Frank Calegari PDF
J. Amer. Math. Soc. 25 (2012), 533-554 Request permission


We prove, under mild hypotheses, that there are no irreducible two-dimensional potentially semi-stable even $p$-adic Galois representations of $\mathrm {Gal}(\overline {\mathbf {Q}})$ with distinct Hodge–Tate weights. This removes the ordinary hypotheses required in the author’s previous work. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric deformations.
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Additional Information
  • Frank Calegari
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
  • MR Author ID: 678536
  • Email:
  • Received by editor(s): January 5, 2011
  • Received by editor(s) in revised form: September 1, 2011
  • Published electronically: October 3, 2011
  • Additional Notes: This research was supported in part by NSF Career Grant DMS-0846285 and the Sloan Foundation.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 533-554
  • MSC (2010): Primary 11R39, 11F80
  • DOI:
  • MathSciNet review: 2869026