Higher F-injective singularities

2024/12/12 by Tatsuro Kawakami, Kawakami, Tatsuro, Jakub Witaszek +1 · 2 citations
Mathematics · #Rings, Modules, and Algebras #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2412.08887

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.

Cited by

• A p-adic Simpson correspondence for singular rigid-analytic varieties
• On Steenbrink vanishing for rational singularities in positive characteristic

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