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On the divisible part of the Brauer group of a field

Author: Tilmann Würfel
Journal: Proc. Amer. Math. Soc. 84 (1982), 173-174
MSC: Primary 12G05; Secondary 20E18
MathSciNet review: 637162
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Abstract: For a field $ k$ and an odd prime $ p \ne \operatorname{char} (k)$ such that the $ p$-primary component $ B{(k)_{(p)}}$ of the Brauer group $ B(k)$ of $ k$ is not zero there exists a finite extension $ k/k$ such that $ B{(k)_{(p)}}$ contains a nontrivial divisible subgroup.

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

  • [1] A. Brumer and M. Rosen, On the size of the Brauer group, Proc. Amer. Math. Soc. 19 (1968), 707-711. MR 0225769 (37:1362)
  • [2] J.-P. Serre, Cohomologie galoisienne, Lecture Notes in Math., vol. 5, 4th ed., Springer-Verlag, Berlin, Heidelberg and New York, 1973. MR 0404227 (53:8030)
  • [3] T. Würfel, Ein Freiheitskriterium für pro-$ p$-Gruppen mit Anwendung auf die Struktur der Brauer-Gruppe, Math. Z. 172 (1980), 81-88. MR 576299 (82c:20057)

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Keywords: Brauer group of a field, profinite group, divisible group
Article copyright: © Copyright 1982 American Mathematical Society

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