Hilbert-Kunz multiplicity of the powers of an ideal
Commutative Algebra
2023-01-12 v2
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.
Keywords
Cite
@article{arxiv.1809.00209,
title = {Hilbert-Kunz multiplicity of the powers of an ideal},
author = {Ilya Smirnov},
journal= {arXiv preprint arXiv:1809.00209},
year = {2023}
}
Comments
Update: Kriti Goel pointed out that I forgot an assumption in a quoted result of Watanabe-Yoshida Theorem 2.8. This forces a revision of Conjecture 2.10