Generalized Hilbert-Kunz Multiplicity for Families of Ideals
Commutative Algebra
2025-10-31 v1
Abstract
In this paper, we initiate a systematic study of the generalized Hilbert-Kunz multiplicity for families of ideals in a Noetherian local ring (R,m) of positive characteristic, and introduce a new asymptotic invariant called the Amao-type multiplicity. We establish that, for a p-family of ideals, the generalized Hilbert-Kunz multiplicity arises as the limit of Amao-type multiplicities.
Keywords
Cite
@article{arxiv.2510.25984,
title = {Generalized Hilbert-Kunz Multiplicity for Families of Ideals},
author = {Stephen Landsittel and Sudipta Das},
journal= {arXiv preprint arXiv:2510.25984},
year = {2025}
}
Comments
27 pages