Period-index and u-invariant questions for function fields over complete discretely valued fields

TL;DR

This paper investigates bounds on the Brauer p-dimension and u-invariant for function fields over complete discretely valued fields, linking these invariants to properties of the residue field, especially in positive characteristic.

Contribution

It establishes new bounds for the Brauer p-dimension and u-invariant of function fields over complete discretely valued fields, particularly in positive characteristic cases.

Findings

Bound for Brauer p-dimension in terms of p-rank of residue field

u-invariant of function field is at most 8 in characteristic 2

Results connect invariants of function fields with residue field properties

Abstract

Let K be a complete discretely valued field and F the function field of a curve over K. If the characteristic of the residue field k of K is p > 0, then we give a bound for the Brauer p-simension of F in terms of the p-rank of k. If k is a perfect field of characteristic 2, we show that the u-invaraint of F is at most 8.