Prismatic cohomology and de Rham-Witt forms
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866915430781681664 |
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| author | Molokov, Semen |
| author_facet | Molokov, Semen |
| contents | For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/dϕ(d)\cdotsϕ^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it is an isomorphism. Using this result, we obtain an explicit description of the prismatic cohomology for a $p$-completed polynomial algebra over $A/d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_04956 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Prismatic cohomology and de Rham-Witt forms Molokov, Semen Algebraic Geometry Number Theory For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/dϕ(d)\cdotsϕ^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it is an isomorphism. Using this result, we obtain an explicit description of the prismatic cohomology for a $p$-completed polynomial algebra over $A/d$. |
| title | Prismatic cohomology and de Rham-Witt forms |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2008.04956 |