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arXiv · 2208.08016

Quasi-F-splittings in birational geometry

Tatsuro Kawakami·Teppei Takamatsu·Hiromu Tanaka·Jakub Witaszek·Fuetaro Yobuko·Shou Yoshikawa
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Abstract

We develop the theory of quasi-$F$-splittings in the context of birational geometry. Amongst other things, we obtain results on liftability of sections and establish a criterion for whether a scheme is quasi-$F$-split employing the higher Cartier operator. As one of the applications of our theory, we prove that three-dimensional klt singularities in large characteristic are quasi-$F$-split, and so, in particular, they lift modulo $p^2$.

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Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa. 2022-08-17. Quasi-F-splittings in birational geometry. https://arxiv.org/abs/2208.08016

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