Tame and strongly \'etale cohomology of curves

DOI10.1007/S11856-022-2355-XzbMATH Open1522.14026arXiv1911.05595MaRDI QIDQ6329109

Katharina Hübner

Publication date: 13 November 2019

Abstract: For a curve $C$ over a perfect field $k$ of characteristic $p>0$ we study the tame cohomology of $X=extitSpa(C,k)$ 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 'etale cohomology). Using purity we show Poincar'e duality for the tame cohomology of $X$ with $p$-torsion coefficients.

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20)

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