Bounds on the Hilbert-Kunz Multiplicity
Olgur Celikbas, Hailong Dao, Craig Huneke, Yi Zhang
TL;DR
This paper establishes new lower bounds for the Hilbert-Kunz multiplicity in unmixed non-regular local rings, ensuring they are uniformly greater than one, thus advancing understanding of their algebraic properties.
Contribution
It provides improved lower bounds on Hilbert-Kunz multiplicity, refining previous results by Aberbach and Enescu for a specific class of rings.
Findings
Lower bounds are strictly greater than one for certain rings.
Bounds are uniform across classes of unmixed non-regular local rings.
Results improve upon previous bounds by Aberbach and Enescu.
Abstract
In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed non-regular local rings, bounding them uniformly away from one. Our results improve previous work of Aberbach and Enescu.
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Taxonomy
TopicsGraph theory and applications · Rings, Modules, and Algebras · Finite Group Theory Research