EVENT DETAILS AND ABSTRACT

Title: Potential automorphy for certain Galois representations to GL(n)
Speaker: Tom Barnet-Lamb
Speaker Info: Harvard
Brief Description:
Special Note:
Abstract:

I will describe recent generalizations of mine to a theorem of Harris, Shepherd-Barron, and Taylor, showing that certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field. The main innovation is that the result applies to Galois representations to GL_n, where the previous work dealt with representations to Sp_n; I can also relax certain congruence conditions which existed in the earlier work, and work over a CM, rather than a totally-real, field. The main technique is the consideration of the cohomology the Dwork hypersurface, and in particular, of pieces of this cohomology other than the invariants under the natural group action.