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Higher F-injective singularities

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arxiv 2412.08887 v1 pith:URZKHNEF submitted 2024-12-12 math.AG

Tatsuro Kawakami , Jakub Witaszek This is my paper · ORCID
classification math.AG
keywords higherinjectivityapplicationboischaracteristicconceptconjectureconverse
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abstract

We introduce the concept of higher $F$-injectivity, a generalisation of $F$-injectivity. We prove that an isolated singularity over a field of characteristic zero is $k$-Du Bois if it is $k$-$F$-injective after reductions modulo infinitely many primes $p$. Under the ordinarity conjecture, we also establish the converse. As an application, we study Frobenius liftable hypersurfaces.

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  1. On Steenbrink vanishing for rational singularities in positive characteristic

    math.AG 2025-07 conditional novelty 6.0 of 10

    A positive characteristic Steenbrink vanishing theorem is proved for rational singularities, giving the vanishing for strongly F-regular threefolds and Q-factorial klt threefolds in large characteristic.

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