# Mathematics Algebra Seminar: Period-Index Problems over Characteristic $p$

This event is in the past.

**When:**

September 5, 2023

1 p.m. to 2 p.m.

1 p.m. to 2 p.m.

**Where:**

**Event category:**Seminar

In-person

**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 ${bar{mathbb{F}}_p}((t)).$