Tame and strongly étale cohomology of curves

2019/11/13 by Hübner, Katharina
#11G20 #14F20 #14H25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.05595

Abstract

For a curve C over a perfect field k of characteristic p > 0 we study the tame cohomology of X = 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.

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