Year: 2019
Type: other
Abstract: In this expository article we explore the relationship between Galois representations, motivic L 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 g\le 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.
Author: Andrew Sutherland
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2340468191