Cyclic Stickelberger cohomology and descent of Kummer extensions

Childs, Lindsay N.

doi:10.1090/S0002-9939-1984-0733396-2

Cyclic Stickelberger cohomology and descent of Kummer extensions
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Proc. Amer. Math. Soc. 90 (1984), 505-510 Request permission

Abstract:

Let $R$ be a field, $S = R[{\rm {\zeta }}]$, ${\rm {\zeta }}$ an $n$th root of unit, $\Delta = {\rm {Gal(}}S/R)$. The group of cyclic Kummer extensions of $S$ on which $\Delta$ acts, modulo those which descend to $R$, is isomorphic to a group of roots of unity and to a second group cohomology group of $\Delta$ whose definition involves a "Stickelberger element".

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