$F$-nilpotent rings and permanence properties

Abstract

We explore the singularity classes $F$-nilpotent, weakly $F$-nilpotent, and generalized weakly $F$-nilpotent under faithfully flat local ring maps. As an application, we show that the loci of primes in a Noetherian ring of prime characteristic which define either weakly $F$-nilpotent or $F$-nilpotent local rings are open with respect to the Zariski topology whenever $R$ is $F$-finite or essentially of finite type over an excellent local ring.

Improvements to the article have been made

References in corpus (2)

• A sufficient condition for finiteness of Frobenius test exponents
• The gamma construction and asymptotic invariants of line bundles over arbitrary fields

Cited by in corpus (2)

• Generalized $F$-depth and graded nilpotent singularities
• Counting geometric branches via the Frobenius map and $F$-nilpotent singularities