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Patching subfields of division algebras


Authors: David Harbater, Julia Hartmann and Daniel Krashen
Journal: Trans. Amer. Math. Soc. 363 (2011), 3335-3349
MSC (2010): Primary 12F12, 16K20, 14H25; Secondary 16S35, 12E30, 16K50
DOI: https://doi.org/10.1090/S0002-9947-2010-05229-8
Published electronically: December 29, 2010
MathSciNet review: 2775810
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

David Harbater
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email: harbater@math.upenn.edu

Julia Hartmann
Affiliation: Lehrstuhl A für Mathematik, RWTH Aachen University, 52062 Aachen, Germany
Email: hartmann@mathA.rwth-aachen.de

Daniel Krashen
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: dkrashen@math.uga.edu

DOI: https://doi.org/10.1090/S0002-9947-2010-05229-8
Keywords: Admissibility, patching, division algebras, Brauer groups, Galois groups.
Received by editor(s): April 9, 2009
Received by editor(s) in revised form: October 14, 2009
Published electronically: December 29, 2010
Additional Notes: The authors were respectively supported in part by NSF Grant DMS-0500118, the German National Science Foundation (DFG), and an NSA Young Investigator’s Grant.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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