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ISSN 1088-6834(e) ISSN 0894-0347(p)

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
Posted: October 3, 2011
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Abstract: We prove, under mild hypotheses, that there are no irreducible two-dimensional potentially semi-stable even -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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