Étale cohomology of algebraic varieties over Stein compacta

2023/05/10 by Benoist, Olivier
#11E25 #12G10 #14F20 #32A20 #32C05 #32E10 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.06054

Abstract

We prove a comparison theorem between the étale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension n has cohomological dimension n. As an application of \textrmGal(ℂ/ℝ)-equivariant variants of these results, we obtain a quantitative version of Hilbert's 17th problem on compact subsets of real-analytic spaces.

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