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Tame and strongly étale cohomology of curves

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Abstract

For a curve C over a perfect field k of characteristic p > 0 we study the tame cohomology of \(\mathcal{C}\) = Spa(C, k) introduced in [Hüb21]. We prove that the tame cohomology groups of \(\mathcal{C}\) 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 \(\mathcal{C}\) with p-torsion coefficients.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

    Katharina Hübner

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  1. Katharina Hübner
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Correspondence to Katharina Hübner.

Additional information

This research is partly supported by ERC Consolidator Grant 770922 - BirNonArchGeom

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Hübner, K. Tame and strongly étale cohomology of curves. Isr. J. Math. 253, 1–42 (2023). https://doi.org/10.1007/s11856-022-2355-x

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  • DOI: https://doi.org/10.1007/s11856-022-2355-x

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