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# David Geraghty : Modularity lifting beyond the numerical coincidence of Taylor and Wiles

Modularity lifting theorems were introduced by Taylor and Wiles and formed a key part of the proof of Fermat's Last Theorem. Their method has been generalized successfully by a number authors but always with the restriction that the Galois representations in question have regular weight. Moreover, the sought after automorphic representation must come from a group that admits Shimura varieties. I will describe a method to overcome these restrictions, conditional on certain conjectures which themselves can be established in a number of cases. This is joint with Frank Calegari.

**Category**: Algebraic Geometry**Duration**: 01:34:55**Date**: March 27, 2013 at 4:25 PM**Views**: 98-
**Tags:**seminar, Algebraic Geometry Seminar

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