A relative version of Kummer theory

Details A relative version of Kummer theory A relative version of Kummer theory

2008-08-13

arxiv.org/abs/0808.1760v1

Mathematics

Number Theory

6 pages

Scientific paper

Let $E/F$ be a cyclic Galois extension of degree $p^l$ with Galois group $G$.
It is shown that the Galois module structure of both sides of the Kummer
pairing (for Kummer extensions of $E$) are the same. In other words, we show
that the Kummer duality holds in the level of finitely generated $G$-modules.

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