Tight closure and strongly F-regular rings
From MaRDI portal
Publication:2168884
DOI10.1007/s40687-022-00353-zOpenAlexW4292980562MaRDI QIDQ2168884
Publication date: 26 August 2022
Published in: Research in the Mathematical Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40687-022-00353-z
tight closurecluster algebra\(F\)-signatureweakly \(F\)-regular ring\(F\)-rational ringstrongly \(F\)-regular ring\(F\)-regular ring\(F\)-split ringFrobenius endomorphism, Frobenius functorGlassbrenner criterion
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Closure operations that induce big Cohen-Macaulay modules and classification of singularities
- \(F\)-signature exists
- Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
- Tight closure and elements of small order in integral extensions
- The existence of the \(F\)-signature for rings with large \(\mathbb Q\)-Gorenstein locus
- Globally \(F\)-regular and log Fano varieties
- Tight closure does not commute with localization
- Singularités rationnelles et quotients par les groupes réductifs. (Rational singularities and quotients by reductive groups)
- Jacobian ideals and a theorem of Briancon-Skoda
- Infinite integral extensions and big Cohen-Macaulay algebras
- The purity of the Frobenius and local cohomology
- Tight closure of parameter ideals
- Some surprising Hilbert-Kunz functions
- Ringe der Charakteristik p und Frobeniusfunktoren
- Tight closure and projective bundles.
- Minimal relative Hilbert-Kunz multiplicity
- The \(F\)-signature and strong \(F\)-regularity.
- Comparison of symbolic and ordinary powers of ideals.
- Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic
- Closure operations that induce big Cohen-Macaulay algebras
- Axiomatic closure operations, phantom extensions, and solidity
- \(F\)-signature and Hilbert-Kunz multiplicity: a combined approach and comparison
- The Hilbert-Kunz function
- Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
- Two theorems about maximal Cohen-Macaulay modules
- Uniform stability of kernels of Koszul cohomology indexed by the Frobenius endomorphism
- Applications of the existence of big Cohen-Macaulay algebras
- Good filtrations and strong \(F\)-regularity of the ring of \(U_P\)-invariants
- Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers
- Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
- Singularities of locally acyclic cluster algebras
- Correction to the article ``Frobenius and valuation rings
- When does the F-signature exist?
- Fine behavior of symbolic powers of ideals
- Observations on the \(F\)-signature of local rings of characteristic \(p\)
- Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
- What makes a complex exact?
- On the commutation of the test ideal with localization and completion
- A characterization of closure operations that induce big Cohen-Macaulay modules
- F-Pure Homomorphisms, StrongF-regularity, andF-injectivity
- F-rational rings have rational singularities
- Absolute integral closures are big Cohen-Macaulay algebras in characteristic 𝑃
- Tight closure and strong F-regularity
- Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
- Big Cohen-Macaulay algebras and seeds
- F-Purity and Rational Singularity
- Tightly closed ideals
- Localization of tight closure and modules of finite phantom projective dimension.
- On Noetherian Rings of Characteristic p
- Cyclic Purity Versus Purity in Excellent Noetherian Rings
- A characterization of rational singularities in terms of injectivity of Frobenius maps
- F-Regularity, Test Elements, and Smooth Base Change
- Slopes of vector bundles on projective curves and applications to tight closure problems
- Content of local cohomology, parameter ideals, and robust algebras
- Uniform bounds in F-finite rings and lower semi-continuity of the F-signature
- Homological Conjectures and Lim Cohen-Macaulay Sequences
- Phantom homology
- Strong F-regularity in images of regular rings
- Strong and weak F -regularity are equivalent for graded rings
- Characterizations of Regular Local Rings of Characteristic p
- Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
- Contracted ideals from integral extensions of regular rings
- Application des techniques $L^2$ à la théorie des idéaux d'une algèbre de fonctions holomorphes avec poids
- A characterization of rational singularities
- Good filtrations of symmetric algebras and strong F-regularity of invariant subrings.
- Uniform bounds and symbolic powers on smooth varieties
- Localization and test exponents for tight closure
- Globally F-regular varieties: Applications to vanishing theorems for quotients of Fano varieties
