Liftability and vanishing theorems for Fano threefolds in positive characteristic I

Tatsuro Kawakami; Hiromu Tanaka

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arXiv · 2503.10236

Liftability and vanishing theorems for Fano threefolds in positive characteristic I

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 for the case when $|-K_X|$ is very ample and the Picard group is generated by $ω_X$.

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Tatsuro Kawakami, Hiromu Tanaka. 2026-08-25. Liftability and vanishing theorems for Fano threefolds in positive characteristic I. https://arxiv.org/abs/2503.10236

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