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Pré-Publication, Document De Travail Année : 2023

Étale cohomology of algebraic varieties over Stein compacta

Résumé

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 Gal(C/R)-equivariant variants of these results, we obtain a quantitative version of Hilbert's 17th problem on compact subsets of real-analytic spaces.

Dates et versions

hal-04234662 , version 1 (10-10-2023)

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Olivier Benoist. Étale cohomology of algebraic varieties over Stein compacta. 2023. ⟨hal-04234662⟩
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