A moving lemma for cohomology with support

authored by

Stefan Schreieder

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.

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

Type

Preprint

Publication date

17.07.2022

Publication status

Elektronisch veröffentlicht (E-Pub)

Electronic version(s)

https://doi.org/10.48550/arXiv.2207.08297 (Access: Offen)