A moving lemma for cohomology with support
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911718698909696 |
|---|---|
| author | Schreieder, Stefan |
| author_facet | Schreieder, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08297 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A moving lemma for cohomology with support Schreieder, Stefan Algebraic Geometry K-Theory and Homology 14C15, 14C25, 14F20 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. |
| title | A moving lemma for cohomology with support |
| topic | Algebraic Geometry K-Theory and Homology 14C15, 14C25, 14F20 |
| url | https://arxiv.org/abs/2207.08297 |