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arXiv · 2207.08297

A moving lemma for cohomology with support

Stefan Schreieder
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Abstract

For a natural class of cohomology theories with support (including \'etale or pro-\'etale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit a smooth projective compactification (e.g. if char(k)=0). This has the following consequences for such k-varieties and cohomology theories: a local and global generalization of the effacement theorem of Quillen, Bloch--Ogus, and Gabber, a finite level version of the Gersten conjecture in characteristic zero, and a generalization of the injectivity property and the codimension 1 purity theorem for \'etale cohomology. Our results imply that the refined unramified cohomology groups from [Sch23] are motivic.

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Stefan Schreieder. 2022-07-17. A moving lemma for cohomology with support. https://doi.org/10.46298/epiga.2024.10038

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