Frobenius Test Exponent for Ideals Generated by Filter Regular Sequences

Abstract

Let $(R,\mathfrak m)$ be a Noetherian local ring of prime characteristic p > 0, and t an integer such that $H_{\mathfrak m}^{j}(R)/0^{F}_{H^{j}_{\mathfrak m}(R)}$ 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.