On the divisible part of the Brauer group of a field
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- by Tilmann Würfel PDF
- Proc. Amer. Math. Soc. 84 (1982), 173-174 Request permission
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
- Armand Brumer and Michael Rosen, On the size of the Brauer group, Proc. Amer. Math. Soc. 19 (1968), 707–711. MR 225769, DOI 10.1090/S0002-9939-1968-0225769-2
- Jean-Pierre Serre, Cohomologie Galoisienne, Lecture Notes in Mathematics, Vol. 5, Springer-Verlag, Berlin-New York, 1973. Cours au Collège de France, Paris, 1962–1963; Avec des textes inédits de J. Tate et de Jean-Louis Verdier; Quatrième édition. MR 0404227, DOI 10.1007/978-3-662-21553-1
- Tilmann Würfel, Ein Freiheitskriterium für pro-$p$-Gruppen mit Anwendung auf die Struktur der Brauer-Gruppe, Math. Z. 172 (1980), no. 1, 81–88 (German). MR 576299, DOI 10.1007/BF01182782
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 173-174
- MSC: Primary 12G05; Secondary 20E18
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637162-6
- MathSciNet review: 637162