Potential automorphy for certain Galois representations to GL_2n
Abstract
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.
Cite
@article{arxiv.0811.1586,
title = {Potential automorphy for certain Galois representations to GL_2n},
author = {Thomas Barnet-Lamb},
journal= {arXiv preprint arXiv:0811.1586},
year = {2010}
}
Comments
37 pages, 1 figure; essentially final version, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal). This version does not incorporate any minor changes (e.g. typographical changes) made in proof