Sato-Tate Distributions
Number Theory
2021-11-30 v6
Abstract
In this expository article we explore the relationship between Galois representations, motivic L-functions, Mumford-Tate groups, and Sato-Tate groups, and we give an explicit formulation of the Sato-Tate conjecture for abelian varieties as an equidistribution statement relative to the Sato-Tate group. We then discuss the classification of Sato-Tate groups of abelian varieties of dimension g <= 3 and compute some of the corresponding trace distributions. This article is based on a series of lectures presented at the 2016 Arizona Winter School held at the Southwest Center for Arithmetic Geometry.
Cite
@article{arxiv.1604.01256,
title = {Sato-Tate Distributions},
author = {Andrew V. Sutherland},
journal= {arXiv preprint arXiv:1604.01256},
year = {2021}
}
Comments
Minor correction to Section 1.2; 45 pages