Even Galois representations and the Fontaine–Mazur conjecture. II

Calegari, Frank

doi:10.1090/S0894-0347-2011-00721-2

Even Galois representations and the Fontaine–Mazur conjecture. II
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by Frank Calegari

J. Amer. Math. Soc. 25 (2012), 533-554

DOI: https://doi.org/10.1090/S0894-0347-2011-00721-2

Published electronically: October 3, 2011

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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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