Hilbert–Kunz Multiplicity and an Inequality between Multiplicity and Colength☆

By Kei-ichi Watanabe, KEN-ICHI Yoshida. 2000

113 citations recorded by the source corpus.

Abstract In this paper, we study local rings of small Hilbert–Kunz multiplicity. In particular, we prove that an unmixed local ring of Hilbert–Kunz multiplicity one is regular and classify two-dimensional Cohen–Macaulay local rings whose Hilbert–Kunz multiplicity is 2 or less. Also, we investigate the inequality between the multiplicity and the colength of the tight closure of parameter ideals inverse to the usual inequality between multiplicity and colength.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0edbbb0f8e5d75405c9d932697c83a31db51448d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Two theorems about maximal Cohen–Macaulay modules (2002, methodology): “s(R) = 1. Conversely suppose that s(R) = 1. Then Proposition 14 proves that eHK(R) = 1. Since Cohen–Macaulay rings are automatically unmixed, we obtain from [ 18 ] that R is regular.”