TY - JOUR

T1 - Projective Schur groups of Henselian fields

AU - Aljadeff, Eli

AU - Sonn, Jack

AU - Wadsworth, Adrian R.

N1 - Funding Information:
The research was supported by the Fund for the Promotion of Research at the Technion.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33751327556&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2006.03.019

DO - 10.1016/j.jpaa.2006.03.019

M3 - 文章

AN - SCOPUS:33751327556

SN - 0022-4049

VL - 208

SP - 833

EP - 851

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -