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What is The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails about?

We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for terminal 3-folds in characteristic $p \in \left\{2, 3, 5\right\}$. To prove this, we introduce the notion of $\mathbb{F}_p$-rationality for singularities in positive characteristic and we show that klt singularities in dimension at most 4 are $\mathbb{F}_p$-rational. We apply this to prove a Frobenius-stable version of the Kawamata-Viehweg vanishing theorem on $K$-trivial 3-folds.

Author

Baudin, Jefferson; Bernasconi, Fabio; Kawakami, Tatsuro

Published

2023

Language

EN