On isomorphisms between deformation rings and Hecke rings, by Chandrashekhar Khare

In this paper we give three different proofs of the theorems of Wiles (and Taylor) that do not make use of Taylor-Wiles systems. Two of the proofs make use of level lowering results modulo high powers of p, while one uses a more traditional monodromy argument.

Chandrashekhar Khare <shekhar@math.tifr.res.in>