### Galois Seminar

Friday, September 27, 2019 - 3:15pm

#### Saurabh Gosavi

Rutgers University

Location

University of Pennsylvania

DRL 4N30

Given a finite set of Brauer classes B of a fixed period \ell, we define eind(B) to be the minimum of degrees of field extensions L/F such that \alpha \otimes_F L = 0 for every \alpha in B. We provide upper-bounds for eind(B) which depends on invariants of fields of lower arithmetic complexity, for B in the Brauer group of a semi-global field. As a simple application of our result, we obtain upper-bound for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields.