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 $H_{\mathfrak{m}}^j(R)/0_{H_{\mathfrak{m}}^j(R)}^F$ 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 $t$.

To appear in Acta Mathematica Vietnamica