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

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.

22 pages