Relative Brauer groups and m-torsion

Eli Aljadeff*, Jack Sonn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 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 m-torsion 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 two-dimensional local field K = k((t)) and m = 2.

Original languageEnglish
Pages (from-to)1333-1337
Number of pages5
JournalProceedings of the American Mathematical Society
Volume130
Issue number5
DOIs
StatePublished - 2002
Externally publishedYes

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