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arXiv · 2506.01345

Quasi-canonical lifting of projective varieties in positive characteristic

Ryo Ishizuka·Kazuma Shimomoto
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Abstract

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.

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Ryo Ishizuka, Kazuma Shimomoto. 2025-06-02. Quasi-canonical lifting of projective varieties in positive characteristic. https://arxiv.org/abs/2506.01345

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