Henselian valued quasilocal fields with totally indivisible value groups, II

TL;DR

This paper characterizes certain Henselian valued quasilocal fields with totally indivisible value groups, focusing on their Brauer groups and the existence of finite separable extensions with nontrivial defect, revealing specific realizability conditions.

Contribution

It provides a detailed characterization of quasilocal fields with totally indivisible value groups, especially regarding their Brauer groups and defect properties, extending prior classifications.

Findings

Realizable Brauer groups depend on prime q and the structure of T.

Finite separable extensions with nontrivial defect exist in these fields.

Specific conditions exclude q=2 with trivial 2-component of T.

Abstract

This paper characterizes the quasilocal fields from the class of Henselian valued fields with totally indivisible value groups, which possess finite separable extensions of nontrivial defect. We show that, for any prime number $q$, a divisible subgroup $T$ in the multiplicative group of complex numbers is realizable as the Brauer group of such a quasilocal field of residual characteristic $q$ unless $q = 2$ and the $2$-component of T$ is trivial.