On the uniform bound of Frobenius test exponents

2018/04/02 by Quy, Pham Hung
#13A35 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01012

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 Hⁱ_{\frak m}(R), i < dim R, are nilpotent.

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