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

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This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal of R, there is a power Q of p, depending on, such that the Q-th Frobenius power of the Frobenius closure of is equal to the Q-th Frobenius power of. The paper addresses the question as to whether there exists a uniform Q₀ 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 Q₀ when R is Cohen--Macaulay. The purpose of this paper is to show that such a uniform Q₀ 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.