Publications at the Riemann Center

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)