title: Deforming semistable Galois representations.
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.
authors.affiliation: Université de Paris-Sud, Mathématique, Bâtiment 425, F-91405 Orsay Cedex, France.
authors.forename: J M
authors.initials: JM
authors.lastname: Fontaine