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Liftability and vanishing theorems for Fano threefolds in positive characteristic I

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arxiv 2503.10236 v2 pith:E4LYD7IP submitted 2025-03-13 math.AG

Tatsuro Kawakami , Hiromu Tanaka This is my paper · ORCID
classification math.AG
keywords characteristicfanopositivethreefoldsvanishingakizuki-nakanoamplecase
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abstract

In our series of papers, we prove that smooth Fano threefolds in positive characteristic lift to the ring of Witt vectors. Moreover, we show that they satisfy Akizuki-Nakano vanishing, $E_1$-degeneration of the Hodge to de Rham spectral sequence, and torsion-freeness of Crystalline cohomologies. In this paper, we establish these results for the case when $|-K_X|$ is very ample and the Picard group is generated by $\omega_X$.

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  1. Frobenius liftable hypersurfaces

    math.AG 2025-07 accept novelty 7.0 of 10

    Frobenius-liftable reduced divisors in projective space are exactly toric divisors, up to automorphism.

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