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The localization spectral sequence in the motivic setting

Clément Dupont and Daniel Juteau

Algebraic & Geometric Topology 24 (2024) 1431–1466

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 –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.

cohomology, motives, spectral sequences
Mathematical Subject Classification
Primary: 18N40
Secondary: 14F42, 14N20
Received: 18 February 2021
Revised: 22 June 2022
Accepted: 22 January 2023
Published: 28 June 2024
Clément Dupont
Institut Montpelliérain Alexander Grothendieck
Université de Montpellier, CNRS
Daniel Juteau
Université de Picardie Jules Verne, CNRS

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