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arXiv · 1708.00318

A generalization of Serre's condition (F) with applications to the finiteness of unramified cohomology

Igor A. Rapinchuk
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Abstract

In this paper, we introduce a condition $\mathrm{(F}_m'\mathrm{)}$ on a field $K$, for a positive integer $m$, that generalizes Serre's condition (F) and which still implies the finiteness of the Galois cohomology of finite Galois modules annihilated by $m$ and algebraic $K$-tori that split over an extension of degree dividing $m$, as well as certain groups of \'etale and unramified cohomology. Various examples of fields satisfying $\mathrm{(F}_m'\mathrm{)}$, including those that do not satisfy (F), are given.

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BibTeXRIS

Igor A. Rapinchuk. 2017-07-28. A generalization of Serre's condition (F) with applications to the finiteness of unramified cohomology. https://arxiv.org/abs/1708.00318

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