Projective Schur groups of Henselian fields |
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Authors: | Eli Aljadeff Adrian R Wadsworth |
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Institution: | Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel Department of Mathematics, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0112, USA |
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Abstract: | One of the open questions that has emerged in the study of the projective Schur group of a field F is whether or not is an algebraic relative Brauer group over F, i.e. does there exist an algebraic extension L/F such that ? We show that the same question for the Schur group of a number field has a negative answer. For the projective Schur group, no counterexample is known. In this paper we prove that is an algebraic relative Brauer group for all Henselian valued fields F of equal characteristic whose residue field is a local or global field. For this, we first show how is determined by for an equicharacteristic Henselian field with arbitrary residue field k. |
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Keywords: | 11R52 11S25 12F05 12G05 13A20 |
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