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Some computations of the generalized Hilbert-Kunz function and multiplicity


Authors: Hailong Dao and Kei-ichi Watanabe
Journal: Proc. Amer. Math. Soc. 144 (2016), 3199-3206
MSC (2010): Primary 13A35; Secondary 13D07, 13H10
DOI: https://doi.org/10.1090/proc/12928
Published electronically: April 13, 2016
MathSciNet review: 3503689
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Abstract: Let $ R$ be a local ring of characteristic $ p>0$ which is $ F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation type, toric rings, and weakly $ F$-regular rings.


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Additional Information

Hailong Dao
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7523
Email: hdao@ku.edu

Kei-ichi Watanabe
Affiliation: Department of Mathematics, College of Human and Science, Nihon University, Setagaya, Tokyo, 156-0045, Japan
Email: watanabe@math.chs.nihon-u.ac.jp

DOI: https://doi.org/10.1090/proc/12928
Keywords: Frobenius endomorphism, generalized Hilbert-Kunz multiplicity, toric rings, isolated singularity
Received by editor(s): March 3, 2015
Received by editor(s) in revised form: July 28, 2015
Published electronically: April 13, 2016
Additional Notes: The first author was partially supported by NSF grant 1104017
The second author was partially supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Number 26400053
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society

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