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arXiv · 1604.01256

Sato-Tate Distributions

Andrew V. Sutherland
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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.

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Andrew V. Sutherland. 2016-04-05. Sato-Tate Distributions. https://doi.org/10.1090/conm%2F740%2F14904

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