Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular
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Publication:2759010
DOI10.1090/S0002-9939-01-06113-5zbMath0990.13011arXivmath/0209291MaRDI QIDQ2759010
Publication date: 10 December 2001
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0209291
Multiplicity theory and related topics (13H15) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Regular local rings (13H05)
Related Items (19)
Bounds on the Hilbert-Kunz multiplicity ⋮ Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension ⋮ Equimultiplicity in Hilbert-Kunz theory ⋮ On rings with small Hilbert-Kunz multiplicity ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ On lower bounds for \(s\)-multiplicities ⋮ Globalizing F-invariants ⋮ Dual \(F\)-signature of Cohen-Macaulay modules over rational double points ⋮ Hilbert-Kunz multiplicity of products of ideals ⋮ On the upper semi-continuity of the Hilbert-Kunz multiplicity ⋮ Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings ⋮ Observations on the \(F\)-signature of local rings of characteristic \(p\) ⋮ Characterizations of regular local rings in positive characteristics ⋮ Upper semi-continuity of the Hilbert–Kunz multiplicity ⋮ On the Frobenius Power and Colon Ideals ⋮ Equimultiplicity theory of strongly \(F\)-regular rings ⋮ The shape of Hilbert-Kunz functions ⋮ The F-rational signature and drops in the Hilbert-Kunz multiplicity ⋮ The rationality of the Hilbert-Kunz multiplicity in graded dimension two
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