Notes on endomorphisms, local cohomology and completion

IF 0.3 4区数学 Q4 MATHEMATICS Journal of Commutative Algebra Pub Date : 2021-05-03 DOI:10.1090/conm/773/15540

P. Schenzel

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引用次数: 3

Abstract

Let M M denote a finitely generated module over a Noetherian ring R R . For an ideal I ⊂ R I \subset R there is a study of the endomorphisms of the local cohomology module H I g ( M ) , g = g r a d e ( I , M ) , H^g_I(M), g = grade(I,M), and related results. Another subject is the study of left derived functors of the I I -adic completion Λ i I ( H I g ( M ) ) \Lambda ^I_i(H^g_I(M)) , motivated by a characterization of Gorenstein rings given in [25]. This provides another Cohen-Macaulay criterion. The results are illustrated by several examples. There is also an extension to the case of homomorphisms of two different local cohomology modules.

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关于自同态、局部上同调和补全的注解

设M M表示诺瑟环rr上有限生成的模。对于理想I∧R I \子集R，研究了局部上同模H I g (M)， g = g R ade(I,M)， H^g_I(M)， g = grade(I,M)的自同态及其相关结果。另一个主题是研究I - I进补全Λ I I(H I g (M)) \Lambda ^I_i(H^g_I(M))的左衍生函子，其动机是在[25]中给出的Gorenstein环的表征。这提供了另一个科恩-麦考利标准。通过几个实例说明了结果。对于两个不同的局部上同模的同态也有一个推广。

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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.

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