Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Relative Brauer groups and $m$-torsion


Authors: Eli Aljadeff and Jack Sonn
Journal: Proc. Amer. Math. Soc. 130 (2002), 1333-1337
MSC (2000): Primary 11R52, 11S25, 12F05, 12G05
Published electronically: November 9, 2001
MathSciNet review: 1879954
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $K$ be a field and $Br(K)$ its Brauer group. If $L/K$ is a field extension, then the relative Brauer group $Br(L/K)$ is the kernel of the restriction map $res_{L/K}:Br(K)\rightarrow Br(L)$. A subgroup of $Br(K)$ is called an algebraic relative Brauer group if it is of the form $Br(L/K)$ for some algebraic extension $L/K$. In this paper, we consider the $m$-torsion subgroup $Br_{m}(K)$consisting of the elements of $Br(K)$ killed by $m$, where $m$ is a positive integer, and ask whether it is an algebraic relative Brauer group. The case $K=\mathbb{Q} $ is already interesting: the answer is yes for $m$ squarefree, and we do not know the answer for $m$arbitrary. A counterexample is given with a two-dimensional local field $K=k((t))$ and $m=2$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11R52, 11S25, 12F05, 12G05

Retrieve articles in all journals with MSC (2000): 11R52, 11S25, 12F05, 12G05


Additional Information

Eli Aljadeff
Affiliation: Department of Mathematics, Technion, 32000 Haifa, Israel
Email: aljadeff@math.technion.ac.il

Jack Sonn
Affiliation: Department of Mathematics, Technion, 32000 Haifa, Israel
Email: sonn@math.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06286-4
PII: S 0002-9939(01)06286-4
Received by editor(s): November 20, 2000
Published electronically: November 9, 2001
Additional Notes: This research was supported by the Fund for the Promotion of Research at the Technion
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society