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Even Galois representations and the Fontaine–Mazur conjecture. II

Author: Frank Calegari
Journal: J. Amer. Math. Soc. 25 (2012), 533-554
MSC (2010): Primary 11R39, 11F80
Published electronically: October 3, 2011
MathSciNet review: 2869026
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Abstract: 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

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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.