A tight closure approach to arithmetic Macaulayfication
type: Item
instance of: scholarly article
title: A tight closure approach to arithmetic Macaulayfication
zbMATH Open document ID: 0910.13005
author: Ian M. Aberbach
author: Craig Huneke
author: K. E. Smith
published in: Illinois Journal of Mathematics
publication date: 1999-04-22T00:00:00Z
review text: Here is the main result of this paper: Let \(R\) be an excellent normal local ring of prime characteristic and of dimension \(d\). Let \(J\) be an ideal generated of a system of parameters which are test elements (as defined in the theory of tight closure). Then the Rees algebra \(R[Jt]\) is Cohen-Macaulay. This theorem implies the existence of an arithmetic Macaulayfication if \(R\) has an isolated non-\(F\)-rational point, in particular, if \(R\) has an isolated singularity. The existence of an arithmetic Macaylayfication in the case of an isolated singularity follows from the work of M. Brodmann and of S. Goto and K. Yamagishi. However, the methods of this paper are different. The authors use tight closure, especially some variant of ``colon-capturing''.
reviewed by: Moshe Roitman
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 926197
zbMATH Keywords: colon capturing
zbMATH Keywords: desingularization
zbMATH Keywords: Cohen-Macaulay Rees algebra
zbMATH Keywords: prime characteristic
zbMATH Keywords: test elements
zbMATH Keywords: tight closure
zbMATH Keywords: Macaulayfication
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 926197