\(F\)-regularity and \(F\)-purity of graded rings
type: Item
instance of: scholarly article
title: \(F\)-regularity and \(F\)-purity of graded rings
zbMATH Open document ID: 0844.13003
author: Nobuo Hara
published in: Journal of Algebra
publication date: 1995-06-14T00:00:00Z
review text: For a Noetherian ring \(R\) of characteristic \(p > 0\), the notions of \(F\)-purity and \(F\)-regularity are defined using the Frobenius action on \(R\) and the notion of tight closure. This paper gives several necessary and sufficient conditions for a normal graded ring \(R = R(X,D)\) to be either \(F\)-regular or \(F\)-pure, where \(X = \text{Proj} (R)\) is a normal complete intersection subvariety of projective space over a perfect field \(k\) of characteristic \(p > 0\) and \(D\) is a rational coefficient divisor on \(X\).
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 763929
zbMATH Keywords: \(F\)-purity
zbMATH Keywords: \(F\)-regularity
zbMATH Keywords: Frobenius action
zbMATH Keywords: tight closure
zbMATH Keywords: graded ring
zbMATH Keywords: complete intersection
reviewed by: David F. Anderson
MaRDI profile type: Publication
full work available at URL: jabr.1995.1071
OpenAlex ID: W2036068038
DOI: 10.1006/JABR.1995.1071
description: scientific article; zbMATH DE number 763929