Hilbert-Kunz Functions for Normal Rings

2004/04/30 by Craig Huneke, Moira A. McDermott, Paul Monsky · 1 citation
Mathematics · #math.AC #msc:13D40

paper · pdf

published as Math. Res. Letters 11 (2004), no. 4, 539-546 · 11 pages, minor changes, additional references

arxiv created 2004/11/05 · arxiv updated 2009/12/01

Abstract

Let (R,m,k) be an excellent, local, normal ring of characteristic p with a perfect residue field and dim R=d. Let M be a finitely generated R-module. We show that there exists a real number beta(M) such that lambda(M/I^[q]M) = e_HK(M) q^d + beta(M) q^d-1 + O(q^d-2).

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• Hilbert-Kunz series, F-signature series, and weak p-fractals

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