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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
Email: fcale@math.northwestern.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2011-00721-2
PII: S 0894-0347(2011)00721-2
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.