Hilbert-Kunz Functions for Normal Rings

Details Hilbert-Kunz Functions for Normal Rings Hilbert-Kunz Functions for Normal Rings

2004-04-08

arxiv.org/abs/math/0404191v2

Math. Res. Letters 11 (2004), no. 4, 539-546

Mathematics

Commutative Algebra

11 pages, minor changes, additional references

Scientific paper

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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