Liftability and vanishing theorems for Fano threefolds in positive characteristic II

2024/04/07 by Kawakami, Tatsuro, Tanaka, Hiromu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.04764

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, E₁-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 ω_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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