Frobenius test exponent for ideals generated by filter regular sequences

TL;DR

This paper establishes a uniform bound for Frobenius test exponents of ideals generated by filter regular sequences in certain Noetherian local rings of prime characteristic, advancing understanding of Frobenius actions in local cohomology.

Contribution

It proves the existence of a uniform bound for Frobenius test exponents for ideals generated by filter regular sequences of bounded length in specified local rings.

Findings

Existence of a uniform Frobenius test exponent bound

Applicable to ideals generated by filter regular sequences

Advances understanding of Frobenius actions in local cohomology

Abstract

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