Over one year ago, Andrew Wiles announced that he could prove Fermat's Last Theorem by establishing the Taniyama-Shimura Conjecture for a large class of elliptic curves over Q. His proposed proof of the TS Conjecture is based on a reduction of this conjecture to a statement about deformations of mod p Galois representations which arise from modular forms.
T is an isomorphism.
It has been known for some time that the required assertion follows from the statement that T is a complete intersection ring. Earlier thisweek, Richard Taylor and Andrew Wiles announced that they could prove precisely this, thereby establishing Fermat's Last Theorem. I hope to discuss these matters in my talk.