The Hilbert-Kunz function in graded dimension two

Abstract

Let R denote a two-dimensional normal standard-graded domain over the algebraic closure K of a finite field of characteristic p, and let I denote a homogeneous primary ideal. We prove that the Hilbert-Kunz function of I has the form = e_{HK}(I) q^{2} + g (q) with rational Hilbert-Kunz multiplicity e_{HK}(I) and an eventually periodic function g (q).

References in corpus (1)

• The rationality of the Hilbert-Kunz multiplicity in graded dimension two

Cited by in corpus (4)

• Hilbert-Kunz Functions for Normal Rings
• On the arithmetic of tight closure
• Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz fnctions
• p-Fractals and power series--II. Some applications to Hilbert-Kunz theory