Number Theory Seminar

Speaker: Zhenghui Li

Title: On p-torsions of geometric Brauer groups

Abstract: Let X be a smooth projective irreducible variety over a finitely generated field k of characteristic p>0. We show that the finiteness of the exponent of the p-primary part of the geometric Brauer group is equivalent to the Tate conjecture for divisors, generalizing D'Addezio's theorem for abelian varieties to arbitrary smooth projective varieties. In this talk, I will explain how syntomic cohomology is used to prove such a statement. This is a joint work with Yanshuai Qin.