Details
| Original language | English |
|---|---|
| Article number | 20 |
| Number of pages | 50 |
| Journal | Epijournal de Geometrie Algebrique |
| Volume | 2024 |
| Issue number | 20 |
| Early online date | 17 Jul 2022 |
| Publication status | Published - 2024 |
Abstract
Keywords
- math.AG, math.KT, 14C15, 14C25, 14F20, Algebraic cycles, unramified cohomology, Chow groups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
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In: Epijournal de Geometrie Algebrique, Vol. 2024, No. 20, 20, 2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A moving lemma for cohomology with support
AU - Schreieder, Stefan
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - math.AG
KW - math.KT
KW - 14C15, 14C25, 14F20
KW - Algebraic cycles
KW - unramified cohomology
KW - Chow groups
UR - http://www.scopus.com/inward/record.url?scp=85215437090&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2207.08297
DO - 10.48550/arXiv.2207.08297
M3 - Article
VL - 2024
JO - Epijournal de Geometrie Algebrique
JF - Epijournal de Geometrie Algebrique
IS - 20
M1 - 20
ER -