Frobenius test exponent for ideals generated by filter regular sequences

Abstract

Let (R, m) be a Noetherian local ring of prime characteristic p > 0, and t an integer such that H j m (R)/0 F H j m (R) has finite length for all j < t. The aim of this paper is to show that there exists an uniform bound for Frobenius test exponents of ideals generated by filter regular sequences of length at most t. H i m (R) , consists nilpotent elements of H i m (R) under the Frobenius action. The Hartshorne-Speiser-Lyubeznik number