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2017 Geometry on totally separably closed schemes
Stefan Schröer
Algebra Number Theory 11(3): 537-582 (2017). DOI: 10.2140/ant.2017.11.537

Abstract

We prove, for quasicompact separated schemes over ground fields, that Čech cohomology coincides with sheaf cohomology with respect to the Nisnevich topology. This is a partial generalization of Artin’s result that for noetherian schemes such an equality holds with respect to the étale topology, which holds under the assumption that every finite subset admits an affine open neighborhood (AF-property). Our key result is that on the absolute integral closure of separated algebraic schemes, the intersection of any two irreducible closed subsets remains irreducible. We prove this by establishing general modification and contraction results adapted to inverse limits of schemes. Along the way, we characterize schemes that are acyclic with respect to various Grothendieck topologies, study schemes all local rings of which are strictly henselian, and analyze fiber products of strict localizations.

Citation

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Stefan Schröer. "Geometry on totally separably closed schemes." Algebra Number Theory 11 (3) 537 - 582, 2017. https://doi.org/10.2140/ant.2017.11.537

Information

Received: 24 March 2015; Revised: 18 October 2016; Accepted: 18 November 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 06722475
MathSciNet: MR3649361
Digital Object Identifier: 10.2140/ant.2017.11.537

Subjects:
Primary: 14F20
Secondary: 13B22, 13J15, 14E05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 3 • 2017
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