On pp-adic geometric representations of GQG_{\mathbb{Q}}.

  • J.-P. Wintenberger


A conjecture of Fontaine and Mazur states that a geometric odd irreducible pp-adic representation ρ\rho of the Galois group of Q\Bbb Q comes from a modular form ([FM95]). Dieulefait proved that, under certain hypotheses, ρ\rho is a member of a compatible system of \ell-adic representations, as predicted by the conjecture ([Dieu]). Thanks to recent results of Kisin (Mark), we are able to apply the method of Dieulefait under weaker hypotheses. This is useful in the proof of Serre's conjecture (Serre) given in KW1, K,KW2,KW3.