Kiran Kedlaya
Title: Sato-Tate groups of abelian varieties and other motives
Abstract: The Sato-Tate conjecture for elliptic curves, now proved over totally real fields, predicts the distribution of the characteristic polynomials of Frobenius at "random" primes. There is a trichotomy between elliptic curves with complex multiplication (CM) over the base field, with CM over a large field, or without CM. We describe an analogous conjecture for abelian surfaces which predicts a corresponding distribution in terms of a certain compact Lie group (the Sato-Tate group). This group can take any of 52 different forms. Joint work with Francesc Fite, Victor Rotger, and Drew Sutherland.