Spectral sequences in unstable higher homotopy theory and applications to the coniveau filtration
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908364006490112 |
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| author | Déglise, Frédéric Pawar, Rakesh |
| author_facet | Déglise, Frédéric Pawar, Rakesh |
| contents | With the aim of understanding Morel's result on the $\mathbb{A}^1$-homotopy sheaves over a field, we extend the theory of unstable spectral sequences of Bousfield and Kan in the $\infty$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral sequences in unstable higher homotopy theory and applications to the coniveau filtration Déglise, Frédéric Pawar, Rakesh Algebraic Geometry With the aim of understanding Morel's result on the $\mathbb{A}^1$-homotopy sheaves over a field, we extend the theory of unstable spectral sequences of Bousfield and Kan in the $\infty$-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. |
| title | Spectral sequences in unstable higher homotopy theory and applications to the coniveau filtration |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.10111 |