# Seminars & Colloquia Calendar

Algebra Seminar

## Generalized Brauer dimension and other arithmetic invariants of semi-global fields

#### Saurabh Gosavi (Rutgers)

Location:  Hill 525
Date & time: Wednesday, 25 September 2019 at 2:00PM - 3:00PM

Abstract:  Given a finite set of Brauer classes B of a fixed period $$ell$$, we define ind(B) to be the g.c.d of degrees of field extensions L/F such that $alpha otimes L=0$ for every alpha in B. We provide upper-bounds for ind(B) which depends upon arithmetic invariants of fields of lower arithmetic complexity. As a simple application of our result, we will obtain upper-bounds for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields.

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