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 = eHK(I) q2 + g (q) with rational Hilbert-Kunz multiplicity eHK(I) and an eventually periodic function g (q).
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