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Minimal gamma-sheaves

Manuel Blickle

Number 33
Author Manuel Blickle
Year 2009

In this note we show that finitely generated unit OX[σ]--modules for X regular and F--finite have a minimal root (in the sense of [Lyubeznik, F-modules] Definition~3.6). This problem was posed by Lyubeznik and answered by himself in the case that X=Spec R is a complete local ring.
One immediate consequence of this result is that the parameter test module of tight closure theory commutes with localization. As a further application of the methods in this paper we give new proofs of the results on discreteness and rationality of F--thresholds [arXiv:0705.1210] and on D-module generation [arXiv:math/0502405v1]. The new proofs are valid in a slightly more general setting such that they also party cover the generalizations recently obtained in [arXiv:0706.3028].

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