Extension of weakly and strongly F-regular rings by flat maps
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Publication:5945584
DOI10.1006/jabr.2001.8785zbMath1007.13002arXivmath/0209251OpenAlexW2009708294MaRDI QIDQ5945584
Publication date: 22 March 2003
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0209251
Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Extension theory of commutative rings (13B02)
Related Items (26)
A sufficient condition for strong $F$-regularity ⋮ Mathematical biography of Melvin Hochster ⋮ Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension ⋮ F-thresholds, tight closure, integral closure, and multiplicity bounds ⋮ When is tight closure determined by the test ideal? ⋮ A New Version of α-Tight Closure ⋮ Characterization of varieties of Fano type via singularities of Cox rings ⋮ Remarks on the small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules ⋮ Frobenius splitting, strong F-regularity, and small Cohen-Macaulay modules ⋮ Openness of splinter loci in prime characteristic ⋮ Big tight closure test elements for some non-reduced excellent rings ⋮ Cohomology and geometry of Deligne-Lusztig varieties for \(\mathrm{GL}_n\) ⋮ A length characterization of \(*\)-spread ⋮ Phantom depth and flat base change ⋮ Hilbert-Kunz density function for graded domains ⋮ \(F\)-signature of pairs and the asymptotic behavior of Frobenius splittings ⋮ Reductions and special parts of closures ⋮ The cl-core of an ideal ⋮ Observations on the \(F\)-signature of local rings of characteristic \(p\) ⋮ Behavior of test ideals under smooth and étale homomorphisms. ⋮ Hilbert-Kunz density function and Hilbert-Kunz multiplicity ⋮ A formula for the *-core of an ideal ⋮ The structure of \(F\)-pure rings ⋮ Central elements in affine modpHecke algebras via perverse -sheaves ⋮ \(\star\)-independence and special tight closure. ⋮ Test ideals and base change problems in tight closure theory
Cites Work
- Tight closure and elements of small order in integral extensions
- Infinite integral extensions and big Cohen-Macaulay algebras
- On the behavior of F-rational rings under flat base change
- On the commutation of the test ideal with localization and completion
- Tight closure and strong F-regularity
- Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
- On Noetherian Rings of Characteristic p
- Cyclic Purity Versus Purity in Excellent Noetherian Rings
- F-regularity does not deform
- F-Regularity, Test Elements, and Smooth Base Change
- Contracted ideals from integral extensions of regular rings
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