Title: Hilbert-Kunz functions of modules over a Noetherian ring regular in codimension one

Abstract: Let R be an excellent local ring of characteristic
p, dim R = d and assume R has a perfect residue field.
For a finitely generated module M of dimension d,
Monsky (1983) proved the existence of the Hilbert-Kunz multiplicity,
denoted α, and that the Hilbert-Kunz function is in the form of

where q = p

Huneke, McDermott and Monsky (Math. Res. Lett. 11 (2004)
539-546) further proved that if in addition R is normal, then there
exists a constant β such that

for n >> 0 in Z.

In this talk, I will weaken the normality condition on the ring and extend Huneke-McDermott-Monsky's proof to rings that are regular in codimension one. Each finitely generated module defines a unique cycle class in the Chow group (replacing the divisor class group in the normal case). I will demonstrate a useful property on these cycle classes and apply it to achieve the desired proof.