A family of Calabi-Yau varieties and potential automorphy (original) (raw)

Pages 779-813 from Volume 171 (2010), Issue 2

Abstract

We prove potential modularity theorems for lll-adic representations of any dimension. From these results we deduce the Sato-Tate conjecture for all elliptic curves with nonintegral jjj-invariant defined over a totally real field.

Authors

Michael Harris

Centre de Mathématiques de Jussieu
Université Paris 7 Denis Diderot
Case Postale 7012
2, place Jussieu
F-75251 Paris Cedex 05
France

Nick Shepherd-Barron

DPMMS
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
England

Richard Taylor

Department of Mathematics
One Oxford Street
Harvard University
Cambridge, MA 02138
United States