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Journal of Pure and Applied Algebra 208 (2007) 833851 www.elsevier.com/locate/jpaa

Summary: Journal of Pure and Applied Algebra 208 (2007) 833­851
Projective Schur groups of Henselian fields
Eli Aljadeff, Jack Sonn, Adrian R. Wadsworth
Department of Mathematics, Technion­Israel Institute of Technology, 32000 Haifa, Israel
Department of Mathematics, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0112, USA
Received 24 June 2005; received in revised form 17 February 2006; accepted 3 March 2006
Available online 6 June 2006
Communicated by A.V. Geramita
One of the open questions that has emerged in the study of the projective Schur group PS(F) of a field F is whether or not
PS(F) is an algebraic relative Brauer group over F, i.e. does there exist an algebraic extension L/F such that PS(F) = Br(L/F)?
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 PS(F) 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 PS(F) is determined by PS(k)
for an equicharacteristic Henselian field with arbitrary residue field k.
c 2006 Elsevier B.V. All rights reserved.
MSC: 11R52; 11S25; 12F05; 12G05; 13A20
1. Introduction
Let F be a field, and Br(F) its Brauer group. The Schur group S(F) of F is the subgroup of Br(F) consisting of


Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology


Collections: Mathematics