Nonfiniteness of Hilbert–Kunz functions

Here we answer a question of C. Huneke, by giving an example of a family (parametrized by A F ̄ p 1 ) of one-dimensional reduced Cohen–Macaulay rings such that every member has the same Hilbert–Kunz multiplicity but there are infinitely many Hilbert–Kunz functions in the family.

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 127; no. 2; pp. 263 - 268
Main Author TRIVEDI, V
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.04.2017
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Hilbert–Kunz multiplicity
Cohen-Macaulay rings
Hilbert–Kunz functions
13A35, 11T99, 13A02
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Summary:Here we answer a question of C. Huneke, by giving an example of a family (parametrized by A F ̄ p 1 ) of one-dimensional reduced Cohen–Macaulay rings such that every member has the same Hilbert–Kunz multiplicity but there are infinitely many Hilbert–Kunz functions in the family.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-017-0329-4