The localization spectral sequence in the motivic setting

Dupont, Clément; Juteau, Daniel

doi:10.2140/agt.2024.24.1431

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The localization spectral sequence in the motivic setting

Clément Dupont and Daniel Juteau

Algebraic & Geometric Topology 24 (2024) 1431–1466

DOI: 10.2140/agt.2024.24.1431

Abstract

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.

Keywords

cohomology, motives, spectral sequences

Mathematical Subject Classification

Primary: 18N40

Secondary: 14F42, 14N20

References

Publication

Received: 18 February 2021

Revised: 22 June 2022

Accepted: 22 January 2023

Published: 28 June 2024

Authors

Clément Dupont
Institut Montpelliérain Alexander Grothendieck Université de Montpellier, CNRS Montpellier France

Daniel Juteau
LAMFA Université de Picardie Jules Verne, CNRS Amiens France

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Volume 24, issue 3 (2024)