Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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".


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12F10, 13B05

Retrieve articles in all journals with MSC: 12F10, 13B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0733396-2
Article copyright: © Copyright 1984 American Mathematical Society