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摘要翻译：
Smith和Van den Bergh引入了有限F-表示型的概念，作为有限表示型概念的特征$P$类似物。本文证明了有限F-表示型环的两个有限性质。第一个性质是：如果$R=\bigoplus_{n\ge0}R_n$是具有有限（分次）F-表示型的Noetherian分次环，则对于R$中的每个非零除数$x\，$R_x$由$1/x$生成为$D_{R}$-模。第二个结论是：如果$R$是具有有限F-表示型的Gorenstein环，那么对于任何理想的$I$和任何整数$N$,$H_i^n(R)$只有有限多个相关素数。我们还包括关于有限（分次）F-表示型环的理想的F-跳跃指数离散性的一个结果作为附录。
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英文标题：
《D-modules over rings with finite F-representation type》
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作者：
Shunsuke Takagi and Ryo Takahashi
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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：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：
Smith and Van den Bergh introduced the notion of finite F-representation type as a characteristic $p$ analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if $R=\bigoplus_{n \ge 0}R_n$ is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodivisor $x \in R$, $R_x$ is generated by $1/x$ as a $D_{R}$-module. The second one states that if $R$ is a Gorenstein ring with finite F-representation type, then $H_I^n(R)$ has only finitely many associated primes for any ideal $I$ of $R$ and any integer $n$. We also include a result on the discreteness of F-jumping exponents of ideals of rings with finite (graded) F-representation type as an appendix.
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PDF链接：
https://arxiv.org/pdf/0706.3842
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