A moving lemma for cohomology with support
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)
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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.
@article{10_46298_epiga_2024_10038,
author = {Schreieder, Stefan},
title = {A moving lemma for cohomology with support},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
year = {2023},
doi = {10.46298/epiga.2024.10038},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2024.10038/}
}
Schreieder, Stefan. A moving lemma for cohomology with support. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2024.10038
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