A stacky approach to prismatic crystals via $q$-prism charts
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912324362698752 |
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| author | Liu, Zeyu |
| author_facet | Liu, Zeyu |
| contents | Let $Y$ be a locally complete intersection over $\mathcal{O}_K$ containing a $p$-power root of unity $ζ_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent complexes on the prismatization of $Y$ via $q$-prism charts. We also develop a Galois descent mechanism to remove the assumption on $\mathcal{O}_K$. As an application, we classify quasi-coherent complexes on the Cartier-Witt stack and give a purely algebraic calculation of the cohomology of the structure sheaf on the absolute prismatic site of $\mathbb{Z}_p$. Along the way, for $Y$ a locally complete intersection over $\overline{A}$ with $A$ lying over a $q$-prism, we classify quasi-coherent complexes on the relative prismatization of $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A stacky approach to prismatic crystals via $q$-prism charts Liu, Zeyu Algebraic Geometry Number Theory Let $Y$ be a locally complete intersection over $\mathcal{O}_K$ containing a $p$-power root of unity $ζ_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent complexes on the prismatization of $Y$ via $q$-prism charts. We also develop a Galois descent mechanism to remove the assumption on $\mathcal{O}_K$. As an application, we classify quasi-coherent complexes on the Cartier-Witt stack and give a purely algebraic calculation of the cohomology of the structure sheaf on the absolute prismatic site of $\mathbb{Z}_p$. Along the way, for $Y$ a locally complete intersection over $\overline{A}$ with $A$ lying over a $q$-prism, we classify quasi-coherent complexes on the relative prismatization of $Y$. |
| title | A stacky approach to prismatic crystals via $q$-prism charts |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2504.07005 |