A stacky comparison of the Hodge and Nygaard filtrations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913947796373504 |
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| author | Hauck, Maximilian |
| author_facet | Hauck, Maximilian |
| contents | We use the approach to $p$-adic cohomology theories via stacks recently developed by Drinfeld and Bhatt--Lurie to formulate a stacky version of a comparison result between the Nygaard filtration on prismatic cohomology and the Hodge filtration on de Rham cohomology by Bhatt--Lurie and thereby also obtain a generalisation in the case of smooth and proper $p$-adic formal schemes which allows for coefficients in an arbitrary gauge. In the process, we develop a stacky approach to diffracted Hodge cohomology as introduced by Bhatt--Lurie which also captures the conjugate filtration and the Sen operator. In the appendix, we also introduce a stack computing the conjugate filtration on absolute Hodge--Tate cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A stacky comparison of the Hodge and Nygaard filtrations Hauck, Maximilian Algebraic Geometry Number Theory We use the approach to $p$-adic cohomology theories via stacks recently developed by Drinfeld and Bhatt--Lurie to formulate a stacky version of a comparison result between the Nygaard filtration on prismatic cohomology and the Hodge filtration on de Rham cohomology by Bhatt--Lurie and thereby also obtain a generalisation in the case of smooth and proper $p$-adic formal schemes which allows for coefficients in an arbitrary gauge. In the process, we develop a stacky approach to diffracted Hodge cohomology as introduced by Bhatt--Lurie which also captures the conjugate filtration and the Sen operator. In the appendix, we also introduce a stack computing the conjugate filtration on absolute Hodge--Tate cohomology. |
| title | A stacky comparison of the Hodge and Nygaard filtrations |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2505.03546 |