Stability and deformation of $F$-singularities

Cites Work

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Nilpotence of Frobenius action and the Hodge filtration on local cohomology
$F$-signature exists
Algebricite de certains points singuliers algebroides
Generalized test ideals, sharp $F$-purity, and sharp test elements
Frobenius splitting and cohomology vanishing for Schubert varieties
The invariance of Hilbert functions of quotients under small perturbations
The purity of the Frobenius and local cohomology
Singularités rationnelles et déformations
Weak F-regularity deforms in $\mathbb{Q}$-Gorenstein rings
Deformation of F-purity and F-regularity
Tight closure of parameter ideals
The height of ideals and regular sequences
$F$-signature and Hilbert-Kunz multiplicity: a combined approach and comparison
Frobenius splitting methods in geometry and representation theory
Openness of the F-rational locus and smooth base change
Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
The F-rational signature and drops in the Hilbert-Kunz multiplicity
On semicontinuity of multiplicities in families
Filter regular sequence under small perturbations
Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
Finite determinacy of matrices and ideals
Rational singularities, with applications to algebraic surfaces and unique factorization
Deformation of F-injectivity and local cohomology
F-Pure Homomorphisms, StrongF-regularity, andF-injectivity
FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION
F-rational rings have rational singularities
Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
F-Purity and Rational Singularity
Secondary representations for injective modules over commutative Noetherian rings
On Noetherian Rings of Characteristic p
A characterization of rational singularities in terms of injectivity of Frobenius maps
F-regularity does not deform
F-Regularity, Test Elements, and Smooth Base Change
SOME CONDITIONS FOR THE EQUIVALENCE OF WEAK AND STRONG F-REGULARITY
$F$-singularities in families
A uniform treatment of Grothendieck's localization problem
ERRATUM: CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE
An analogue of adjoint ideals and PLT singularities in mixed characteristic
CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE
Introduction to Singularities
Local cohomology of Du Bois singularities and applications to families
Characterizations of Regular Local Rings of Characteristic p
When does a perturbation of the equations preserve the normal cone?
$F$-nilpotent rings and permanence properties
F-Purity Deforms in ℚ-Gorenstein Rings
The theory of F-rational signature
Permanence properties of $F$-injectivity

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Stability and deformation of \(F\)-singularities