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

TL;DR
This paper characterizes which finite groups can be Galois groups of maximal subfields of division algebras over certain function fields, using patching techniques to extend previous partial results.
Contribution
It provides a complete characterization of such Galois groups over function fields of curves over complete discretely valued fields with algebraically closed residue fields, employing patching methods.
Findings
Complete classification of Galois groups over specified function fields
Extension of Schacher's partial results to new cases
Application of patching techniques in division algebra context
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 over the field of rational numbers. 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation
