 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 130, Number 5, Pages 13331337
S 00029939(01)062864
Article electronically published on November 9, 2001
RELATIVE BRAUER GROUPS AND mTORSION
ELI ALJADEFF AND JACK SONN
(Communicated by David E. Rohrlich)
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 re
striction map resL/K : Br(K) 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 mtorsion subgroup Brm(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 = 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 twodimensional
local field K = k((t)) and m = 2.
1. Introduction
Let K be a field and Br(K) its Brauer group. If L/K is a field extension, then
