Potential automorphy for certain Galois representations to GL_2n

Details Potential automorphy for certain Galois representations to GL_2n Potential automorphy for certain Galois representations to GL_2n

2008-11-10

arxiv.org/abs/0811.1586v4

Mathematics

Number Theory

37 pages, 1 figure; essentially final version, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journa

Scientific paper

Building upon work of Clozel, Harris, Shepherd-Barron, and Taylor, this paper shows that certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field. The main innovation here is that the result applies to Galois representations to GL_{2n}, where previous work dealt with representations to GSp_n. 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.

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