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arXiv · 2412.08887

Higher F-injective singularities

Tatsuro Kawakami·Jakub Witaszek
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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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Tatsuro Kawakami, Jakub Witaszek. 2024-12-12. Higher F-injective singularities. https://arxiv.org/abs/2412.08887

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