摘要翻译：
设$(R，\Mathfrak m)$表示一个$N$维Gorenstein环。对于高度为$C$的理想$I\子集R$，我们对自同态环$B=\HOM_R(H^C_I(R),H^C_I(R))感兴趣。在$(R，\Mathfrak m)$的情况下，包含字段$B$的正则局部环是Cohen-Macaulay环。它的性质与最大Lyubeznik数$L=\dim_k\ext_r^d(k,h^c_i(R)).特别是$R\simeq b$当且仅当$L=1.并且我们证明了$\ext_r^d(k,h^c_i(R))\到k$的自然同态是非零的。
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英文标题：
《On Lyubeznik's invariants and endomorphisms of local cohomology modules》
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作者：
Peter Schenzel
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最新提交年份：
2009
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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：
  Let $(R, \mathfrak m)$ denote an $n$-dimensional Gorenstein ring. For an ideal $I \subset R$ of height $c$ we are interested in the endomorphism ring $B = \Hom_R(H^c_I(R), H^c_I(R)).$ It turns out that $B$ is a commutative ring. In the case of $(R,\mathfrak m)$ a regular local ring containing a field $B$ is a Cohen-Macaulay ring. Its properties are related to the highest Lyubeznik number $l = \dim_k \Ext_R^d(k,H^c_I(R)).$ In particular $R \simeq B$ if and only if $l = 1.$ Moreover, we show that the natural homomorphism $\Ext_R^d(k, H^c_I(R)) \to k$ is non-zero.
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PDF链接：
https://arxiv.org/pdf/0704.2007