Jan Minac, Andrew Schultz, John Swallow: Galois module structure of pth-power classes of cyclic extensions of degree p^n

minac@uwo.ca, aschultz@stanford.edu, joswallow@davidson.edu

Submission: 2004, Oct 30

In the mid-1960s Borevi\v{c} and Faddeev initiated the study of the Galois module structure of groups of $p$th-power classes of cyclic extensions $K/F$ of $p$th-power degree. They determined the structure of these modules in the case when $F$ is a local field. In this paper we determine these Galois modules for all base fields $F$.

2000 Mathematics Subject Classification: 12F10, 16D70

Keywords and Phrases: cyclic extension, Galois module, Hilbert 90, Kummer theory, multiplicative group of a field, norm

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