Projective Schur groups of Henselian fields

Eli Aljadeff, Jack Sonn, Adrian R. Wadsworth*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)833-851
Number of pages19
JournalJournal of Pure and Applied Algebra
Volume208
Issue number3
DOIs
StatePublished - Mar 2007
Externally publishedYes

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