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Hilbert-Kunz multiplicity of the powers of an ideal


Author: Ilya Smirnov
Journal: Proc. Amer. Math. Soc. 147 (2019), 3331-3338
MSC (2010): Primary 13A35, 13H15
DOI: https://doi.org/10.1090/proc/14513
Published electronically: April 8, 2019
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Abstract: We study Hilbert-Kunz multiplicity of the powers of an ideal and establish existence of the second coefficient at the full level of generality, thus extending a recent result of Trivedi. We describe the second coefficient as the limit of the Hilbert coefficients of Frobenius powers and show that it is additive in short exact sequences and satisfies a Northcott-type inequality.


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Additional Information

Ilya Smirnov
Affiliation: Department of Mathematics, Stockholm University, S-106 91, Stockholm, Sweden
Email: smirnov@math.su.se

DOI: https://doi.org/10.1090/proc/14513
Received by editor(s): November 12, 2018
Received by editor(s) in revised form: December 2, 2018
Published electronically: April 8, 2019
Communicated by: Claudia Polini
Article copyright: © Copyright 2019 American Mathematical Society