Associated primes of formal local cohomology modules

TL;DR

This paper investigates the finiteness of associated primes of formal local cohomology modules, establishing conditions under which the associated primes of a specific module are finite based on the support of earlier modules.

Contribution

It proves that finiteness of support for lower-degree formal local cohomology modules implies finiteness of associated primes at a specific degree, advancing understanding of their structure.

Findings

Finiteness of support implies finiteness of associated primes at a certain degree.

Provides conditions linking support and associated primes of formal local cohomology modules.

Enhances understanding of the structure of formal local cohomology in Noetherian rings.

Abstract

Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper we proved that if $\operatorname{Supp}\mathfrak{F}_\mathfrak{a}^i(M)$ is finite for all $i<t$, then so is $\operatorname{Ass}(\mathfrak{F}_{\mathfrak{a}}^t(M))$.