Patching subfields of division algebras

Details Patching subfields of division algebras Patching subfields of division algebras

2009-04-09

arxiv.org/abs/0904.1594v2

Mathematics

Rings and Algebras

20 pages. In Section 3 some statements were strengthened and proofs simplified. At the end of Section 4 the definition of the

Scientific paper

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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