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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.07628 |
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| _version_ | 1866909436903161856 |
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| author | Kothari, Casimir |
| author_facet | Kothari, Casimir |
| contents | We construct smooth projective families of algebraic varieties in characteristic $p$ such that the dimensions of the de Rham and Hodge cohomology groups of the fibers can be made to jump by an arbitrarily large amount. To do this, we first construct an example using the classifying stack of a finite flat group scheme which degenerates $\mathbb{Z}/p^2\mathbb{Z}$ to $α_p \oplus α_p$. Along the way, we give a self-contained exposition of the construction of Godeaux--Serre varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$ Kothari, Casimir Algebraic Geometry Number Theory 14D10 (Primary) 14F40, 14L15 (Secondary) We construct smooth projective families of algebraic varieties in characteristic $p$ such that the dimensions of the de Rham and Hodge cohomology groups of the fibers can be made to jump by an arbitrarily large amount. To do this, we first construct an example using the classifying stack of a finite flat group scheme which degenerates $\mathbb{Z}/p^2\mathbb{Z}$ to $α_p \oplus α_p$. Along the way, we give a self-contained exposition of the construction of Godeaux--Serre varieties. |
| title | Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$ |
| topic | Algebraic Geometry Number Theory 14D10 (Primary) 14F40, 14L15 (Secondary) |
| url | https://arxiv.org/abs/2304.07628 |