Patching subfields of division algebras
arXiv:0904.1594
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.
20 pages. In Section 3 some statements were strengthened and proofs simplified. At the end of Section 4 the definition of the rank two valuation was fixed