A moving lemma for cohomology with support

authored by

Stefan Schreieder

Abstract

For a natural class of cohomology theories with support (including étale or pro-étale 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 étale cohomology. Our results imply that the refined unramified cohomology groups from [Sch23] are motivic.

Organisation(s)

Institut für Algebraische Geometrie

Type

Artikel

Journal

Epijournal de Geometrie Algebrique (EPIGA)

Volume

2024

No. of pages

50

Publication date

2024

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie, Geometrie und Topologie

Electronic version(s)

https://doi.org/10.48550/arXiv.2207.08297 (Access: Offen)
https://doi.org/10.46298/epiga.2024.10038 (Access: Offen)