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)