Brauer $p$-dimension of henselian discretely valued fields over characteristic $p>0$

TL;DR

This paper investigates the Brauer p-dimension of henselian discretely valued fields with residual characteristic p>0 using Kato's Swan conductor, linking the period-index problem to symbol length issues in related abelian groups.

Contribution

It introduces a systematic approach to analyze the Brauer p-dimension via Kato's Swan conductor and connects the period-index problem to symbol length problems in abelian groups.

Findings

Established a method to compute Brauer p-dimension using Kato's Swan conductor.

Linked the period-index problem to symbol length problems in abelian groups.

Provided new insights into the structure of henselian discretely valued fields.

Abstract

We use Kato's Swan conductor to systematically investigate the Brauer $p$-dimension of henselian discretely valued fields of residual characteristic $p>0$. We transform the period-index problem of these fields into the symbol length problem for certain abelian groups relating to Kahler differentials of residue fields.