$F$-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.

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

References in corpus (1)

• F-stable secondary representations and deformation of F-injectivity

Cited by in corpus (1)

• Coherence of absolute integral closures