Generalized Hilbert-Kunz Multiplicity for Families of Ideals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912678081986560 |
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| author | Landsittel, Stephen Das, Sudipta |
| author_facet | Landsittel, Stephen Das, Sudipta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Hilbert-Kunz Multiplicity for Families of Ideals Landsittel, Stephen Das, Sudipta Commutative Algebra 13H15, 13A35 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. |
| title | Generalized Hilbert-Kunz Multiplicity for Families of Ideals |
| topic | Commutative Algebra 13H15, 13A35 |
| url | https://arxiv.org/abs/2510.25984 |