局部上同调模及其子范畴的共性

IF 0.7 2区 数学 Q2 MATHEMATICS
Ryo Takahashi, Naoki Wakasugi
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引用次数: 0

摘要

设R是可交换诺瑟环,I是R的理想环。设对于所有整数I,局部上同模\({\text {H}}_I^i(R)\)是I有限的。假设\(R_\mathfrak {p}\)是一个正则局部环,对于所有不含i的素理想\(\mathfrak {p}\),我们证明了如果i -有限模构成一个阿贝范畴,那么对于所有有限生成的r -模M和所有整数i,局部上同模\({\text {H}}_I^i(M)\)是i -有限的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cofiniteness of local cohomology modules and subcategories of modules

Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the local cohomology module \({\text {H}}_I^i(R)\) is I-cofinite. Suppose that \(R_\mathfrak {p}\) is a regular local ring for all prime ideals \(\mathfrak {p}\) that do not contain I. In this paper, we prove that if the I-cofinite modules form an abelian category, then for all finitely generated R-modules M and all integers i, the local cohomology module \({\text {H}}_I^i(M)\) is I-cofinite.

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来源期刊
Collectanea Mathematica
Collectanea Mathematica 数学-数学
CiteScore
2.70
自引率
9.10%
发文量
36
审稿时长
>12 weeks
期刊介绍: Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.
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