Speaker: Dr. Yuan Yang (Imperial College London)
Time: 10:00-11:00  July 4, 2025 (Friday)
Venue: MCM110

Title: Unipotent torsion in the Brauer group of an abelian variety

Abstract: Let A be an abelian variety of dimension g over an algebraically closed field of characteristic p. This talk will focus on the unipotent part U_A of the p-primary torsion subgroup of the Brauer group Br(A). We first introduce a formula expressing the p^n-torsion of Br(A) in terms of homomorphisms of truncated p-divisible groups when p is not 2. We then use the theory of the Nygaard filtration to give a quick proof that dim(U_A) depends only on the isogeny class of A, and that the p-exponent of U_A is sharply bounded by g-1. It turns out that both methods are equivalent. Finally, we compute dim(U_A[p]) for any principally polarized abelian variety A, and determine the isogeny class of U_A for all abelian 3-folds. This is a joint work with Livia Grammatica and Alexei Skorobogatov.