On the arithmetic of tight closure

DOI10.1090/S0894-0347-05-00514-XzbMath1096.13005arXivmath/0412033OpenAlexW1855444959MaRDI QIDQ5469250

Mordechai Katzman, Holger Brenner

Publication date: 17 May 2006

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412033

Mathematics Subject Classification ID

Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (2)

Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions ⋮ Tight closure does not commute with localization

Uses Software

• CoCoA
• Macaulay2

Cites Work

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• Local cohomological dimension in characteristic p
• Some surprising Hilbert-Kunz functions
• Semi-stability and reduction \(\bmod p\)
• Tight closure and projective bundles.
• Non-standard tight closure for affine \(\mathbb C\)-algebras
• A characteristic zero Hilbert-Kunz criterion for solid closure in dimension two
• Finite criteria for weak \(F\)-regularity
• Ample vector bundles
• Geometric interpretation of tight closure and test ideals
• The multiplier ideal is a universal test ideal
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• A characterization of rational singularities in terms of injectivity of Frobenius maps
• Slopes of vector bundles on projective curves and applications to tight closure problems
• On a Problem of Miyaoka
• P-Ample Bundles and Their Chern Classes

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