$F$-purity deforms in $\mathbb{Q}$-Gorenstein rings

Abstract

We show that $F$-purity deforms in local $\mathbb{Q}$-Gorenstein rings of prime characteristic $p>0$. Furthermore, we show that $F$-purity is $\mathfrak{m}$-adically stable in local Cohen-Macaulay $\mathbb{Q}$-Gorenstein rings.

arXiv commentThe introduction has been rewritten. The article is to appear in International Mathematics Research Notices

References in corpus (5)

• Inversion of adjunction on log canonicity
• Finite torsors over strongly $F$-regular singularities
• Stability and deformation of F-singularities
• Local cohomology bounds and test ideals
• F-stable secondary representations and deformation of F-injectivity

Cited by in corpus (2)

• Coherence of absolute integral closures
• Inversion of adjunction for $F$-signature