2013/10/16 by Timo Hanke, Hanke, Timo, Danny Neftin +3
Mathematics · #12F10 #16S35 (Primary) #16W50 #16W60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1310.4436
openalex publication_date 2013/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.