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

2017/07/28 by Rapinchuk, Igor A.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.00318

Abstract

In this paper, we introduce a condition (F_m') 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 étale and unramified cohomology. Various examples of fields satisfying (F_m'), including those that do not satisfy (F), are given.

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