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arXiv · 0904.1594

Patching subfields of division algebras

David Harbater·Julia Hartmann·Daniel Krashen
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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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David Harbater, Julia Hartmann, Daniel Krashen. 2009-10-23. Patching subfields of division algebras. https://arxiv.org/abs/0904.1594

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