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arXiv · 2404.04764

Liftability and vanishing theorems for Fano threefolds in positive characteristic II

Tatsuro Kawakami·Hiromu Tanaka
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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 except when $|-K_X|$ is very ample and the Picard group is generated by $\omega_X$. To this end, we show that an arbitrary smooth Fano threefold is quasi-$F$-split when the Picard number or the Fano index is larger than one.

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Tatsuro Kawakami, Hiromu Tanaka. 2024-04-07. Liftability and vanishing theorems for Fano threefolds in positive characteristic II. https://arxiv.org/abs/2404.04764

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