Deforming semistable Galois representations.

Fontaine, J M · Proc Natl Acad Sci U S A · 1997

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Abstract

Let V be a p-adic representation of Gal(Q/Q). One of the ideas of Wiles's proof of FLT is that, if V is the representation associated to a suitable autromorphic form (a modular form in his case) and if V' is another p-adic representation of Gal(Q/Q) "closed enough" to V, then V' is also associated to an automorphic form. In this paper we discuss which kind of local condition at p one should require on V and V' in order to be able to extend this part of Wiles's methods.