Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings

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dc.creatorHuneke, Craig
dc.creatorKatzman, Mordechai
dc.creatorSharp, Rodney Y.
dc.creatorYao, Yongwei
dc.date2006-07-06
dc.date.accessioned2026-07-07T07:18:06Z
dc.date.available2026-07-07T07:18:06Z
dc.descriptionThis paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring $R$ of prime characteristic $p$. For a given ideal $\fa$ of $R$, there is a power $Q$ of $p$, depending on $\fa$, such that the $Q$-th Frobenius power of the Frobenius closure of $\fa$ is equal to the $Q$-th Frobenius power of $\fa$. The paper addresses the question as to whether there exists a {\em uniform} $Q_0$ which `works' in this context for all parameter ideals of $R$ simultaneously. In a recent paper, Katzman and Sharp proved that there does exists such a uniform $Q_0$ when $R$ is Cohen--Macaulay. The purpose of this paper is to show that such a uniform $Q_0$ exists when $R$ is a generalized Cohen--Macaulay local ring. A variety of concepts and techniques from commutative algebra are used, including unconditioned strong $d$-sequences, cohomological annihilators, modules of generalized fractions, and the Hartshorne--Speiser--Lyubeznik Theorem employed by Katzman and Sharp in the Cohen--Macaulay case.
dc.descriptionThis is to appear in the Journal of Algebra
dc.identifierhttps://arxiv.org/abs/math/0607160
dc.identifierhttp://arxiv.org/abs/math/0607160
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114180
dc.subjectCommutative Algebra
dc.subject13A35; 13A15; 13D45; 13E05; 13H10; 16S36
dc.titleFrobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings
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