Perfect even modules and the even filtration
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916449861238784 |
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| author | Pstrągowski, Piotr |
| author_facet | Pstrągowski, Piotr |
| contents | Inspired by the work of Hahn-Raksit-Wilson, we introduce a variant of the even filtration which is naturally defined on $\mathbf{E}_{1}$-rings and their modules. We show that our variant satisfies flat descent and so agrees with the Hahn-Raksit-Wilson filtration on ring spectra of arithmetic interest, showing that various "motivic" filtrations are in fact invariants of the $\mathbf{E}_{1}$-structure alone. We prove that our filtration can be calculated via appropriate resolutions in modules and apply it to the study of even cohomology of connective $\mathbf{E}_{1}$-rings, proving vanishing above the Milnor line, base-change formulas, and explicitly calculating cohomology in low weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04685 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perfect even modules and the even filtration Pstrągowski, Piotr Algebraic Topology K-Theory and Homology Inspired by the work of Hahn-Raksit-Wilson, we introduce a variant of the even filtration which is naturally defined on $\mathbf{E}_{1}$-rings and their modules. We show that our variant satisfies flat descent and so agrees with the Hahn-Raksit-Wilson filtration on ring spectra of arithmetic interest, showing that various "motivic" filtrations are in fact invariants of the $\mathbf{E}_{1}$-structure alone. We prove that our filtration can be calculated via appropriate resolutions in modules and apply it to the study of even cohomology of connective $\mathbf{E}_{1}$-rings, proving vanishing above the Milnor line, base-change formulas, and explicitly calculating cohomology in low weights. |
| title | Perfect even modules and the even filtration |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2304.04685 |