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].