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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}
}

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27 pages