Associated primes of local cohomology after adjoining indeterminates. II: The general case
type: Item
instance of: scholarly article
title: Associated primes of local cohomology after adjoining indeterminates. II: The general case
zbMATH Open document ID: 1358.13021
DOI: 10.1216/JCA-2016-8-4-589
author: Hannah Robbins
published in: Journal of Commutative Algebra
publication date: 2017-01-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jca/1477600749
review text: Let \(A\) be a field of characteristic \(0\), \(R\) a formal power series ring over \(A\) and \(I \subset R\) an ideal. Then \textit{G. Lyubeznik} showed that the local cohomology module \(H^j_I(R)\) has only finitely many associated primes [Invent. Math. 113, No. 1, 41--55 (1993; Zbl 0795.13004)]. In the present paper, the author tried to weaken the assumption of \(A\) by using the resolution of singularities of \(\mathrm{Spec } A\). One of his result is the following. Let \(A\) be a finitely generated algebra over a field of characteristic \(0\), \(R\) a formal power series ring or a polynomial ring over \(A\), and \(I \subset R\) an ideal. Assume that \(A\) is a normal domain and that \(A\) has an isolated singularity. Then the local cohomology module \(H_I^j(R)\) has finitely many associated primes.
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 6673504
zbMATH Keywords: associated primes
zbMATH Keywords: local cohomology
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6673504