Galois subfields of tame division algebras
Rings and Algebras
2013-10-17 v1
Abstract
We show that a finite-dimensional tame division algebra D over a Henselian field F has a maximal subfield Galois over F if and only if its residue division algebra has a maximal subfield Galois over the residue field of F. This generalizes the mechanism behind several known noncrossed product constructions to a crossed product criterion for all tame division algebras, and in particular for all division algebras if the residue characteristic is 0. If the residue field is a global field, the criterion leads to a description of the location of noncrossed products among tame division algebras, and their discovery in new parts of the Brauer group.
Keywords
Cite
@article{arxiv.1310.4436,
title = {Galois subfields of tame division algebras},
author = {Timo Hanke and Danny Neftin and Adrian Wadsworth},
journal= {arXiv preprint arXiv:1310.4436},
year = {2013}
}