Prismatic crystals and $q$-Higgs fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914718499733504 |
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| author | Tsuji, Takeshi |
| author_facet | Tsuji, Takeshi |
| contents | Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the $q$-crystalline prism. We also discuss its behavior under the scalar extension by the Frobenius lifting and tensor products, and a global description of the cohomology of a prismatic crystal via Zariski cohomological descent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic crystals and $q$-Higgs fields Tsuji, Takeshi Algebraic Geometry Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the $q$-crystalline prism. We also discuss its behavior under the scalar extension by the Frobenius lifting and tensor products, and a global description of the cohomology of a prismatic crystal via Zariski cohomological descent. |
| title | Prismatic crystals and $q$-Higgs fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.11676 |