Quasi-canonical lifting of projective varieties in positive characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910980228775936 |
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| author | Ishizuka, Ryo Shimomoto, Kazuma |
| author_facet | Ishizuka, Ryo Shimomoto, Kazuma |
| contents | The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by showing a descending property of such Frobenius liftability. We establish a refined form of the classical result due to Mehta-Srinivas on the existence of canonical liftings. For this purpose, we also establish a result on the algebraization of certain $p$-adic formal schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-canonical lifting of projective varieties in positive characteristic Ishizuka, Ryo Shimomoto, Kazuma Algebraic Geometry Commutative Algebra The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by showing a descending property of such Frobenius liftability. We establish a refined form of the classical result due to Mehta-Srinivas on the existence of canonical liftings. For this purpose, we also establish a result on the algebraization of certain $p$-adic formal schemes. |
| title | Quasi-canonical lifting of projective varieties in positive characteristic |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2506.01345 |