The tame site of a scheme

Étale cohomology with non-invertible coefficients has some unpleasant properties, e.g., it is not A^1-homotopy invariant and for constructible coefficients the expected finiteness properties do not hold. In this paper we introduce the `tame site' which is slightly coarser than the étale site. T...

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Bibliographic Details
Published inarXiv.org
Main Authors Hübner, Katharina, Schmidt, Alexander
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.07.2020
Subjects
Coefficients
Homology
Mathematics - Algebraic Geometry
Mathematics - Number Theory
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Summary:Étale cohomology with non-invertible coefficients has some unpleasant properties, e.g., it is not A^1-homotopy invariant and for constructible coefficients the expected finiteness properties do not hold. In this paper we introduce the `tame site' which is slightly coarser than the étale site. Tame cohomology coincides with étale cohomology for invertible coefficients but is better behaved in the general case. The fundamental group of the tame site is the (curve-)tame fundamental group of Wiesend and Kerz/Schmidt. The higher tame homotopy groups hopefully have a better behaviour than the higher étale homotopy groups, which vanish for affine schemes in positive characteristic by a result of Achinger.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.05468