We prove that the generalized Hilbert-Kunz function of a graded module over a two-dimensional standard graded normal -domain over an algebraically closed field of prime characteristic has the form , with rational generalized Hilbert-Kunz multiplicity and a bounded function. Moreover, we prove that if is a -algebra, the limit for of the generalized Hilbert-Kunz multiplicity over the fibers exists, and it is a rational number.

Generalized Hilbert-Kunz function in graded dimension 2

Caminata A.
2018

Abstract

We prove that the generalized Hilbert-Kunz function of a graded module over a two-dimensional standard graded normal -domain over an algebraically closed field of prime characteristic has the form , with rational generalized Hilbert-Kunz multiplicity and a bounded function. Moreover, we prove that if is a -algebra, the limit for of the generalized Hilbert-Kunz multiplicity over the fibers exists, and it is a rational number.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/1030785
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