Discreteness and rationality of \(F\)-thresholds
type: Item
instance of: scholarly article
title: Discreteness and rationality of \(F\)-thresholds
zbMATH Open document ID: 1177.13013
author: Manuel Blickle
author: Mircea Mustaţă
author: K. E. Smith
published in: Michigan Mathematical Journal
publication date: 2009-09-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0607660
review text: Test ideals are positive characteristic analogues of multiplier ideals, see for example [\textit{N. Hara} and \textit{K. Yoshida}, Trans. Am. Math. Soc. 355, No. 8, 3143--3174 (2003; Zbl 1028.13003)]. Because of this relation, it is natural to ask whether properties of multiplier ideals also hold for test ideals. One of the easiest-to-prove properties of multiplier ideals is the fact that the associated jumping numbers are discrete and rational [see for example \textit{L. Ein, R. Lazarsfeld, K. E. Smith} and \textit{D. Varolin}, Duke Math. J. 123, No. 3, 469--506 (2004; Zbl 1061.14003)]. Thus it is natural to ask if the analogous \(F\)-jumping numbers of the test ideal are also discrete and rational. This is in no way obvious. This important paper gives an affirmative answer to this question in the case that the ambient space is regular and essentially of finite type over a perfect field (or even an \(F\)-finite field). The methods of the proof have are themselves both very concrete and extremely interesting. The tools developed in this paper have since spawned further work by several people including the reviewer.
reviewed by: Karl Schwede
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 5604519
zbMATH Keywords: F-threshold
zbMATH Keywords: F-jumping number
zbMATH Keywords: test ideal
zbMATH Keywords: jumping number
zbMATH Keywords: tight closure
zbMATH Keywords: Frobenius power
MaRDI profile type: Publication
OpenAlex ID: W1982865390
arXiv ID: math/0607660
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DOI: 10.1307/MMJ/1220879396
description: scientific article