On Henselian valuations and Brauer groups of primarily quasilocal fields

TL;DR

This paper classifies the Brauer groups of certain Henselian valued primarily quasilocal fields, showing they are divisible and can be embedded into a specific subgroup of rational numbers.

Contribution

It provides a classification of abelian torsion groups that can be realized as Brauer groups of these specialized fields, advancing understanding of their algebraic structure.

Findings

Brauer groups of these fields are divisible.

Brauer groups embed into the quotient of rationals by integers.

Classification is up to isomorphism for these groups.

Abstract

This paper finds a classification, up-to an isomorphism, of abelian torsion groups realizable as Brauer groups of major types of Henselian valued primarily quasilocal fields with totally indivisible value groups. When $E$ is a quasilocal field with such a valuation, it shows that the Brauer group of $E$ is divisible and embeddable in the quotient group of the additive group of rational numbers by the subgroup of integers.