Patching subfields of division algebras

Harbater, David; Hartmann, Julia; Krashen, Daniel

doi:10.1090/S0002-9947-2010-05229-8

Patching subfields of division algebras
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by David Harbater, Julia Hartmann and Daniel Krashen PDF

Trans. Amer. Math. Soc. 363 (2011), 3335-3349 Request permission

Abstract:

Given a field $F$, one may ask which finite groups are Galois groups of field extensions $E/F$ such that $E$ is a maximal subfield of a division algebra with center $F$. This question was originally posed by Schacher, who gave partial results in the case $F = \mathbb Q$. Using patching, we give a complete characterization of such groups in the case that $F$ is the function field of a curve over a complete discretely valued field with algebraically closed residue field of characteristic zero, as well as results in related cases.

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