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arXiv · 1610.00733

Capitulation, unit groups, and the cohomology of $S$-id\`{e}le classes

Saikat Biswas
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Abstract

Let $L/K$ be a finite, cyclic extension of number fields with Galois group $G$, and let $S$ be a finite set of primes of $K$ that includes all the infinite primes. In this paper, we study the $G$-cohomology of the $S$-id\`{e}le classes of $L$ and relate it to the $S$-capitulation map as well as to the $G$-cohomology of the $S$-unit group $U_{L,S}$.

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Saikat Biswas. 2016-10-03. Capitulation, unit groups, and the cohomology of $S$-id\`{e}le classes. https://arxiv.org/abs/1610.00733

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