Projective Schur groups of iterated power series fields

TY - JOUR

T1 - Projective Schur groups of iterated power series fields

AU - Aljadeff, Eli

AU - Sonn, Jack

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

PY - 2003/8/1

Y1 - 2003/8/1

N2 - The Brauer-Witt Theorem states that every Schur algebra over a field K is Brauer equivalent to a cyclotomic algebra. A central conjecture on the projective Schur group of a field is the analogue of this theorem, which asserts that every projective Schur algebra over a field K is Brauer equivalent to a radical algebra. The conjecture is so far known to be true in characteristic p and for local and global fields. The next natural class of fields to test is power series fields over local and global fields. In this paper we verify the conjecture for these fields and more generally for iterated power series fields over local and global fields.

AB - The Brauer-Witt Theorem states that every Schur algebra over a field K is Brauer equivalent to a cyclotomic algebra. A central conjecture on the projective Schur group of a field is the analogue of this theorem, which asserts that every projective Schur algebra over a field K is Brauer equivalent to a radical algebra. The conjecture is so far known to be true in characteristic p and for local and global fields. The next natural class of fields to test is power series fields over local and global fields. In this paper we verify the conjecture for these fields and more generally for iterated power series fields over local and global fields.

UR - http://www.scopus.com/inward/record.url?scp=0037781980&partnerID=8YFLogxK

U2 - 10.1016/S0022-4049(02)00326-2

DO - 10.1016/S0022-4049(02)00326-2

M3 - 文章

AN - SCOPUS:0037781980

SN - 0022-4049

VL - 182

SP - 109

EP - 117

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 2-3

ER -