On the uniform bound of Frobenius test exponents

Pham Hung Quy

On the uniform bound of Frobenius test exponents

Commutative Algebra 2018-10-17 v3

Authors: Pham Hung Quy

Abstract

In this paper we prove the existence of a uniform bound for Frobenius test exponents for parameter ideals of a local ring $(R, \frak m)$ of prime characteristic in the following cases: (1) $R$ is generalized Cohen-Macaulay. Our proof is much more simpler than the original proof of Huneke, Katzman, Sharp and Yao, (2) The Frobenius actions on all lower local cohomologies $H^i_{\frak m}(R)$ , $i < \dim R$ , are nilpotent.

Keywords

Frobenius test exponent uniform bound parameter ideal generalized Cohen-Macaulay ring local cohomology nilpotent Frobenius action

Cite

@article{arxiv.1804.01012,
  title  = {On the uniform bound of Frobenius test exponents},
  author = {Pham Hung Quy},
  journal= {arXiv preprint arXiv:1804.01012},
  year   = {2018}
}

Comments

Final version, to appear in Journal of Algebra. arXiv admin note: text overlap with arXiv:1801.04827

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