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arXiv · 0808.1760

A relative version of Kummer theory

Vahid Shirbisheh
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Abstract

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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Vahid Shirbisheh. 2008-08-13. A relative version of Kummer theory. https://arxiv.org/abs/0808.1760

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