Minimal $gamma$--sheaves
Minimal $gamma$--sheaves
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最小$gamma$--滑轮
DOI：
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发表时间：
2007
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通讯作者：
Manuel Blickle
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文献类型：
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作者：
Manuel Blickle
在这篇注记中，我们证明了$X$正则和$F$有限的有限生成单位$O_X[sigma]$-模有一个极小根(在[Lyubeznik，F-模]定义~3.6的意义下)。这个问题由Lyubeznik提出，并在$X=Spec R$是完全局部环的情况下由他自己回答。
这一结果的一个直接后果是，紧闭包理论的参数测试模块与局部化交换。作为本文方法的进一步应用，我们给出了关于$F$-门限[arxiv：0705.1210]和$D$-模生成[arxiv：ath/0502405v1]的离散性和合理性的结果的新证明。新的证明在稍微更一般的情况下是有效的，这样它们也涵盖了最近在[arxiv：0706.3028]中得到的推广。
In this note we show that finitely generated unit $O_X[sigma]$--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].