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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01902 |
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| _version_ | 1866913677817413632 |
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| author | Muñoz--Bertrand, Rubén |
| author_facet | Muñoz--Bertrand, Rubén |
| contents | We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal or a weakly formal scheme, or for the convergent or the overconvergent de Rham-Witt complex on a smooth scheme over a perfect field of positive characteristic. This enables us to give a new description of convergent and overconvergent isocrystals with a Frobenius structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isocrystals and de Rham-Witt connections Muñoz--Bertrand, Rubén Algebraic Geometry We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal or a weakly formal scheme, or for the convergent or the overconvergent de Rham-Witt complex on a smooth scheme over a perfect field of positive characteristic. This enables us to give a new description of convergent and overconvergent isocrystals with a Frobenius structure. |
| title | Isocrystals and de Rham-Witt connections |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.01902 |