Tame and strongly étale cohomology of curves

For a curve \(C\) over a perfect field \(k\) of characteristic \(p > 0\) we study the tame cohomology of \(X = \textit{Spa}(C,k)\) introduced in arXiv:1801.04776. We prove that the tame cohomology groups of \(X\) with \(p\)-torsion coefficients satisfy cohomological purity (which is not true in f...

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Bibliographic Details
Published inarXiv.org
Main Author Hübner, Katharina
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.04.2020
Subjects
Homology
Purity
Torsion
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Summary:For a curve \(C\) over a perfect field \(k\) of characteristic \(p > 0\) we study the tame cohomology of \(X = \textit{Spa}(C,k)\) introduced in arXiv:1801.04776. We prove that the tame cohomology groups of \(X\) with \(p\)-torsion coefficients satisfy cohomological purity (which is not true in full generality for the étale cohomology). Using purity we show Poincaré duality for the tame cohomology of \(X\) with \(p\)-torsion coefficients.
ISSN:2331-8422