Fontaine J M
Université de Paris-Sud, Mathématique, Bâtiment 425, F-91405 Orsay Cedex, France.
Proc Natl Acad Sci U S A. 1997 Oct 14;94(21):11138-41. doi: 10.1073/pnas.94.21.11138.
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.
设(V)是(Gal(\mathbb{Q}/\mathbb{Q}))的一个(p)-adic表示。怀尔斯对费马大定理证明的思路之一是，如果(V)与一个合适的自守形式（在他的情形下是一个模形式）相关联，并且如果(V')是(Gal(\mathbb{Q}/\mathbb{Q}))的另一个与(V)“足够接近”的(p)-adic表示，那么(V')也与一个自守形式相关联。在本文中，我们讨论为了能够扩展怀尔斯方法的这一部分，对于(V)和(V')在(p)处应该要求哪种局部条件。
