Spectral sequences in unstable higher homotopy theory and applications to the coniveau filtration

2024/11/15 by Déglise, Frédéric, Pawar, Rakesh · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.10111

Abstract

With the aim of understanding Morel's result on the \mathbbA¹-homotopy sheaves over a field, we extend the theory of unstable spectral sequences of Bousfield and Kan in the ∞-categorical setting. With this natural extension, parallel to the classical formalism of cohomology theory with supports, we introduce the notion of cohomotopy theory with supports. We extend the Bloch-Ogus-Gabber theorem for Cohomology theory with supports to that of unstable setting, in order to obtain unstable Gersten (or Cousin) resolutions associated with the coniveau filtration, under suitable assumptions. We apply this theory to motivic homotopy, Nisnevich-local torsors and Artin-Mazur étale homotopy types.

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• Monadic resolutions for generalized spaces

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• Gersten weight structures for motivic homotopy categories; retracts of cohomology of function fields, motivic dimensions, and coniveau spectral sequences
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