Cyclic Stickelberger cohomology and descent of Kummer extensions

Author:
Lindsay N. Childs

Journal:
Proc. Amer. Math. Soc. **90** (1984), 505-510

MSC:
Primary 12F10; Secondary 13B05

DOI:
https://doi.org/10.1090/S0002-9939-1984-0733396-2

MathSciNet review:
733396

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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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Article copyright:
© Copyright 1984
American Mathematical Society