Alternating forms and the Brauer group of a geometric field

Brussel, Eric

doi:10.1090/S0002-9947-07-03988-8

Alternating forms and the Brauer group of a geometric field
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by Eric S. Brussel PDF

Trans. Amer. Math. Soc. 359 (2007), 3025-3069 Request permission

Abstract:

We compute the theory of $H^{2}(G,\mathbb {Q}/\mathbb {Z})$ for any proabelian group $G$, using a natural isomorphism with the group $\operatorname {Alt}(G,\mathbb {Q}/\mathbb {Z})$ of continuous alternating forms. We use this to establish a sort of generic behavioral ideal, or role model, for the Brauer group $\text {Br}(F)$ of a geometric field $F$ of characteristic zero. We show this ideal is attained in several interesting cases.

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