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

Seminar

Speaker

Dr. Saurabh Gosavi (Bar-Ilan University)

Date

28/10/2020 - 11:30 - 10:30Add to Calendar

`2020-10-28 10:30:00``2020-10-28 11:30:00``Generalized Brauer dimension and other arithmetic invariants of semi-global fields``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 b \otimes_F L = 0 for every b in B. We provide upper bounds for eind(B) which depend 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 an upper bound for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields. ================================================ Please see the e-mail announcement or contact the organizer for the Zoom link.``Zoom -- see invitation below``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Zoom -- see invitation below

Abstract

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 b \otimes_F L = 0 for every b in B. We provide upper bounds for eind(B) which depend 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 an upper bound for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields.

================================================

Please see the e-mail announcement or contact the organizer for the Zoom link.

Last Updated Date : 21/10/2020