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 -