Even Galois representations and the Fontaine–Mazur conjecture. II

Calegari, Frank¹

¹Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208

Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 533-554

Résumé

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.

Détail

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

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