Speaker: Yizhen Zhao

Institution: Michigan State University

Abstract: The period-index problem is a longstanding question about the Brauer groups of a field. This problem concerns the order (the period) of an element of the Brauer group and the index which is the gcd of all the degrees of finite splitting fields. I will focus on the $p$-torsion part of Brauer groups over characteristic $p$ and the connection between the Kato's Swan conductor and period-index problems of discretely valued fields. As an application, I will talk about our progress on the period-index problem for the Brauer group of the function field of an algebraic curve over ${bar{mathbb{F}}_p}((t)).$