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arXiv · 1310.4436

Galois subfields of tame division algebras

Timo Hanke·Danny Neftin·Adrian Wadsworth
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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.

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Timo Hanke, Danny Neftin, Adrian Wadsworth. 2013-10-16. Galois subfields of tame division algebras. https://arxiv.org/abs/1310.4436

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