A refinement of the Faltings-Serre method, by Nigel Boston

This paper has appeared in Number theory (Paris, 1992-1993), 61-68, London Math. Soc. Lecture Note Ser. 215, Cambridge Univ. Press, Cambridge, 1995, and so the dvi version has been removed. By interpreting the method of Faltings and Serre, which is useful for classifying elliptic curves of various conductors, in terms of deformations of Galois representations, I simplify and extend its scope. In particular, I use it to investigate the internal structure of deformation spaces by addressing the question of when two representations that agree locally, agree globally.

Nigel Boston <boston@math.uiuc.edu>