Irrational Hilbert-Kunz multiplicities

2013/05/25 by Holger Brenner, Brenner, Holger · 5 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1305.5873

Abstract

We interpret Hilbert-Kunz theory of a graded ring of positive characteristic in terms of Frobenius asymptotic of cohomology of vector bundles on projective varieties. With this method we show that for almost all prime numbers there exist three-dimensional quartic hypersurface domains and modules of finite length with irrational Hilbert-Kunz multiplicity. From this we deduce that also the Hilbert-Kunz multiplicity of a local noetherian domain might be an irrational number.

Cited by

• Hilbert-Kunz multiplicity of quadrics decreases
• Local Okounkov bodies and limits in prime characteristic
• Transcendental Hilbert-Kunz Multiplicities
• On the (LC) conjecture
• Length of local cohomology of powers of ideals
• On generalized Hilbert-Kunz function and multiplicity

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