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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
Publication
Received: 18 February 2021
Revised: 22 June 2022
Accepted: 22 January 2023
Published: 28 June 2024
© 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY) .
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