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摘要翻译：
本文研究正则局部环主理想的跳跃系数。最近M.Blickle、M.Mustata和K.Smith证明，当域上的$R$本质上是有限型而$F$是有限型时，有界区间包含有限多个跳跃系数，这些跳跃系数是有理的。在后来的论文中，他们将这些结果推广到$F$-有限完全正则局部环的主理想。本文的目的是将这些关于跳跃系数离散性和合理性的结果推广到含有正特征域的任意（即不一定是f$-有限）优正则局部环的主理想。我们的证明使用了一种非常不同的方法：我们不使用$D$-模，而是在一些非标准Frobenius作用下分析内射壳或$R$中幂零元的模。这种新方法无疑具有更多的应用前景。
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英文标题：
《On the discreteness and rationality of F-jumping coefficients》
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作者：
Mordechai Katzman, Gennady Lyubeznik, Wenliang Zhang
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最新提交年份：
2008
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分类信息：
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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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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英文摘要：
This paper studies the jumping coefficients of principal ideals of regular local rings. Recently M. Blickle, M. Mustata and K. Smith showed that, when $R$ is of essentially finite type over a field and $F$-finite, bounded intervals contain finitely many jumping coefficients and that those are rational. In a later paper they extended these results to principal ideals of $F$-finite complete regular local rings. The aim of this paper is to extend these results on the discreteness and rationality of jumping coefficients to principal ideals of arbitrary (i.e. not necessarily $F$-finite) excellent regular local rings containing fields of positive characteristic. Our proof uses a very different method: we do not use $D$-modules and instead we analyze the modules of nilpotents elements in the injective hull or $R$ under some non-standard Frobenius actions. This new method undoubtedly holds a potential for more applications.
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PDF链接：
https://arxiv.org/pdf/0706.3028
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