A note on Hilbert-Kunz multiplicity

2016/03/14 by Mohsen Asgharzadeh, Asgharzadeh, Mohsen
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1603.04297

Comments are welcome

arxiv created 2016/03/14 · arxiv updated 2016/03/15

Abstract

In this note we first give a new bound on e_HK(∼) the Hilbert-Kunz multiplicity of invariant rings, by the help of the Noether's bound. Then, we simplify, extend and present applications of the reciprocity formulae due to L. Smith. He proved the formula over polynomial rings and his result is tight in the following sense: Over complete intersection rings with isolated singularity we show that the reciprocity formulae "e_HK(R/I)+ e_HK(R/J) = e_HK(R/\underlinef)" is equivalent with \pd(I)<∞ when I is an \fm-primary unmixed ideal linked to J along with a regular sequence \underlinef.

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