The F-signature of an affine semigroup ring

DOI10.1016/j.jpaa.2004.08.001zbMath1080.13001arXivmath/0409143OpenAlexW1965067799MaRDI QIDQ1770538

Anurag K. Singh

Publication date: 7 April 2005

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409143

zbMATH Keywords

positive characteristicF-signatureHilbert-Kunz multiplicitiesaffine semigroup ringrank of a maximal free direct summand

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items

When does the F-signature exist? ⋮ The direct sum decomposability of \(^eM\) in dimension 2 ⋮ The number of torsion divisors in a strongly F-regular ring is bounded by the reciprocal of F-signature ⋮ On the behavior of \(F\)-signatures, splitting primes, and test modules under finite covers ⋮ Globalizing F-invariants ⋮ Purity of monoids and characteristic-free splittings in semigroup rings ⋮ Tame fundamental groups of pure pairs and Abhyankar's lemma ⋮ F-signature function of quotient singularities ⋮ The existence of the \(F\)-signature for rings with large \(\mathbb Q\)-Gorenstein locus ⋮ \(F\)-signature exists ⋮ Observations on the \(F\)-signature of local rings of characteristic \(p\) ⋮ Local Okounkov bodies and limits in prime characteristic ⋮ The uniform symbolic topology property for diagonally \(F\)-regular algebras ⋮ The lower semicontinuity of the Frobenius splitting numbers ⋮ Generalized \(F\)-signatures of Hibi rings ⋮ Differential symmetric signature in high dimension ⋮ The shape of Hilbert-Kunz functions ⋮ Quantifying singularities with differential operators ⋮ Lower bounds on Hilbert–Kunz multiplicities and maximal F-signatures

Cites Work

• Minimal relative Hilbert-Kunz multiplicity
• The \(F\)-signature and strong \(F\)-regularity.
• The Hilbert-Kunz function
• Two theorems about maximal Cohen-Macaulay modules
• When does the F-signature exist?
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Simplicity of Rings of Differential Operators in Prime Characteristic
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes
• Contracted ideals from integral extensions of regular rings
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