Prismatic Crystals for schemes in characteristic $p$
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917729987985408 |
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| author | Yu, Jiahong |
| author_facet | Yu, Jiahong |
| contents | In this paper, we consider the (crystalline) prismatic crystals on a scheme $\mathfrak{X}$. We classify the crystals by $p$-connections on a certain ring and prove a cohomological comparison theorem. This equivalence is more general than the Ogus' equivalence. Moreover, we will prove the equivalence between the crystalline crystals and prismatic crystals by gluing local Ogus-Vologodsky correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic Crystals for schemes in characteristic $p$ Yu, Jiahong Algebraic Geometry Number Theory In this paper, we consider the (crystalline) prismatic crystals on a scheme $\mathfrak{X}$. We classify the crystals by $p$-connections on a certain ring and prove a cohomological comparison theorem. This equivalence is more general than the Ogus' equivalence. Moreover, we will prove the equivalence between the crystalline crystals and prismatic crystals by gluing local Ogus-Vologodsky correspondence. |
| title | Prismatic Crystals for schemes in characteristic $p$ |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2407.15381 |