Seminar| Institute of Mathematical Sciences
Time：Monday, Apirl 3rd, 2023, 10:00-11:30
Location：RS408, IMS
Speaker: Yanshuai Qin , UC Berkeley
Abstract: Let $\mathcal{X} \rightarrow C$ be a dominant morphism between smooth geometrically connected varieties over a finitely generated field such that the generic fiber $X/K$ is smooth, projective and geometrically connected. We prove a relation between the Tate-Shafarevich group of $Pic^0_{X/K}$ and the geometric Brauer groups of $ \mathcal{X}$ , $X$ and $C$, generalizing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary relative dimension.