# MATH Seminar

Title: Generalized Brauer dimension of semi-global fields
Seminar: Algebra
Speaker: Saurabh Gosavi of Rutgers University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2019-11-12 at 4:00PM
Venue: MSC W303
Abstract:
Given a finite set of Brauer classes $B$ of a fixed period $\ell$, we define $ind(B)$ to be the minimum of degrees of field extensions $L/F$ such that $\alpha \otimes_F L = 0$ for every $\alpha$ in $B$. When $F$ is a semi-global field (i.e transcendence degree one field over a complete discretely valued field), we will provide an upper-bound for $ind(B)$ which depends on invariants of fields of lower arithmetic complexity. As a simple application of our result, we will obtain an upper-bound for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields.