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Submission: 2006, Mar 23
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.
2000 Mathematics Subject Classification: 16K20
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