On the Sato-Tate conjecture for non-generic abelian surfaces

Abstract

We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fite, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.

21 pages. Minor changes and corrections. With an appendix by Francesc Fité. Essentially final version, to appear in Transactions of the AMS