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

TL;DR

This paper proves numerous non-generic cases of the Sato-Tate conjecture for abelian surfaces by applying potential automorphy theorems, advancing understanding of the conjecture's scope.

Contribution

It extends the verification of the Sato-Tate conjecture to many non-generic abelian surfaces using advanced automorphy techniques.

Findings

Proved many non-generic cases of the Sato-Tate conjecture for abelian surfaces.

Utilized potential automorphy theorems to establish new cases.

Enhanced the understanding of the distribution of Frobenius elements in 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.