A moving lemma for cohomology with support

Research output: Working paper/Preprint › Preprint

Authors

  • Stefan Schreieder

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Original languageEnglish
Publication statusE-pub ahead of print - 17 Jul 2022

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 [Sch21b] are motivic.

Keywords

    math.AG, math.KT, 14C15, 14C25, 14F20

Cite this

A moving lemma for cohomology with support. / Schreieder, Stefan.
2022.

Research output: Working paper/Preprint › Preprint

Schreieder S. A moving lemma for cohomology with support. 2022 Jul 17. Epub 2022 Jul 17. doi: 10.48550/arXiv.2207.08297
Schreieder, Stefan. / A moving lemma for cohomology with support. 2022.
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