Cousin complex on the complement to the strict normal-crossing divisor in a~local essentially smooth scheme over a~field
Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 210-225
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For any $\mathbb{A}^1$-invariant cohomology theory that satisfies Nisnevich excision on the category of smooth schemes over a field $k$ it is proved that the Cousin complex on the complement $U-D$ to the strict normal-crossing divisor $D$ in a local essentially smooth scheme $U$ is acyclic. This claim is also proved for the schemes $(X-D)\times(\mathbb{A}^1_k-Z_0)\times\dots\times(\mathbb{A}^1_k-Z_l)$, where $Z_0,\dots,Z_l$ is a finite family of closed subschemes in the affine line over $k$.
Bibliography: 32 titles.
Keywords:
Gersten conjecture, Cousin complex, motivic cohomologies.
@article{SM_2023_214_2_a3,
author = {A. E. Druzhinin},
title = {Cousin complex on the complement to the strict normal-crossing divisor in a~local essentially smooth scheme over a~field},
journal = {Sbornik. Mathematics},
pages = {210--225},
publisher = {mathdoc},
volume = {214},
number = {2},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2023_214_2_a3/}
}
TY - JOUR AU - A. E. Druzhinin TI - Cousin complex on the complement to the strict normal-crossing divisor in a~local essentially smooth scheme over a~field JO - Sbornik. Mathematics PY - 2023 SP - 210 EP - 225 VL - 214 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2023_214_2_a3/ LA - en ID - SM_2023_214_2_a3 ER -
%0 Journal Article %A A. E. Druzhinin %T Cousin complex on the complement to the strict normal-crossing divisor in a~local essentially smooth scheme over a~field %J Sbornik. Mathematics %D 2023 %P 210-225 %V 214 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2023_214_2_a3/ %G en %F SM_2023_214_2_a3
A. E. Druzhinin. Cousin complex on the complement to the strict normal-crossing divisor in a~local essentially smooth scheme over a~field. Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 210-225. http://geodesic.mathdoc.fr/item/SM_2023_214_2_a3/