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摘要翻译：
在这篇注释中，我们证明有限生成单元$O_x[\sigma]$-对于$x$regular和$f$-有限的模有一个极小根（在[Lyubeznik,f-模]定义~3.6)。这个问题是由Lyubeznik提出的，并在$x=\spec r$是一个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，我们对$F$-阈值[ARXIV:0705.1210]和$D$-模生成[ARXIV:Math/0502405V1]的离散性和合理性的结果给出了新的证明。新的证明在稍一般的情况下是有效的，因此它们也涵盖了最近在[ARXIV:0706.3028]中得到的概括。
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英文标题：
《Minimal $\gamma$--sheaves》
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作者：
Manuel Blickle
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
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].
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PDF链接：
https://arxiv.org/pdf/0706.4060
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