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4.0
36 reviewsAbstract
We prove a comparison theorem between the étale cohomology of algebraic varietiesover Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Steincompact 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 obtaina quantitative version of Hilbert’s 17th problem on compact subsets of real-analyticspaces.
