Henselian valued quasilocal fields with totally indivisible value groups, II

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.

18 pages, Theorem 1.2, the main result of the paper, is complemented by Propositions 5.1 and 5.2

References in corpus (2)

• Primarily quasilocal fields and 1-dimensional abstract local class field theory
• Demushkin groups and inverse Galois theory for pro-p-groups of finite rank and maximal p-extensions