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We construct and study a motivic lift of a spectral sequence associated to a stratified scheme, recently discovered by Petersen in the context of mixed Hodge theory and ℓ–adic Galois representations. The original spectral sequence expresses the compactly supported cohomology of an open stratum in terms of the compactly supported cohomology of the closures of strata and the combinatorics of the poset underlying the stratification. Some of its special cases are classical tools in the study of arrangements of subvarieties and configuration spaces. Our motivic lift lives in the triangulated category of étale motives and takes the shape of a Postnikov system. We describe its connecting morphisms and study some of its functoriality properties.
Dupont, Clément 1 ; Juteau, Daniel 2
@article{10_2140_agt_2024_24_1431,
author = {Dupont, Cl\'ement and Juteau, Daniel},
title = {The localization spectral sequence in the motivic setting},
journal = {Algebraic and Geometric Topology},
pages = {1431--1466},
publisher = {mathdoc},
volume = {24},
number = {3},
year = {2024},
doi = {10.2140/agt.2024.24.1431},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1431/}
}
TY - JOUR AU - Dupont, Clément AU - Juteau, Daniel TI - The localization spectral sequence in the motivic setting JO - Algebraic and Geometric Topology PY - 2024 SP - 1431 EP - 1466 VL - 24 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1431/ DO - 10.2140/agt.2024.24.1431 ID - 10_2140_agt_2024_24_1431 ER -
%0 Journal Article %A Dupont, Clément %A Juteau, Daniel %T The localization spectral sequence in the motivic setting %J Algebraic and Geometric Topology %D 2024 %P 1431-1466 %V 24 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1431/ %R 10.2140/agt.2024.24.1431 %F 10_2140_agt_2024_24_1431
Dupont, Clément; Juteau, Daniel. The localization spectral sequence in the motivic setting. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1431-1466. doi: 10.2140/agt.2024.24.1431
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