|Title: Generalized Brauer dimension of semi-global fields|
|Speaker: Saurabh Gosavi of Rutgers University|
|Contact: David Zureick-Brown, email@example.com|
|Date: 2019-11-12 at 4:00PM|
|Venue: MSC W303|
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.
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