深度与局部上同调群支集的判定
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摘要
给出了深度的一些等价刻画,这些刻画与支集和局部上同调等概念自然地联系起来.利用滤正则序列和深度的概念讨论了与局部上同调有关的群的支集,给出了一个关于零阶局部上同调群支集是否包含于一个给定闭集的判定方法,同时考虑了高阶局部上同调群支集是否包含于一个给定闭集的情形.
Some equivalent descriptions of depth are given.These descriptions are naturally connected with support and local cohomology.The support of a local cohomological group is studied by the application of the concept of filter regular sequence and depth.A criterion is given for determining whether the support of a 0-th cohomological group is contained in a given closed set.In addition,the similar problem for higher order cohomological groups is discussed.
Some equivalent descriptions of depth are given.These descriptions are naturally connected with support and local cohomology.The support of a local cohomological group is studied by the application of the concept of filter regular sequence and depth.A criterion is given for determining whether the support of a 0-th cohomological group is contained in a given closed set.In addition,the similar problem for higher order cohomological groups is discussed.
引文
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[5]张英龙,李思泽.滤正则序列与局部上同调[J].郑州大学学报:理学版,2012,44(2):6-9.
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[2]Liu Q.Algebraic geometry and arithmetic curves:Oxford graduate texts in mathematics[M].Ern′e R,Translated.Oxford:Oxford University Press,2002.
[3]Bruns W,Herzog J.Cohen-Macaulay rings:Cambridge studies in advanced mathematics[M].Cambridge:Cambridge University Press,1993.
[4]LüRencai,Tang Zhongming.The f-depth of an ideal on a module[J].Proceedings of the American Mathematical Society,2002,130(7):1905-1912.
[5]张英龙,李思泽.滤正则序列与局部上同调[J].郑州大学学报:理学版,2012,44(2):6-9.
[6]Matsumura H.Commutative ring theory[M].Reid M,Translated.Cambridge:Cambridge University Press,1989.
[7]Weibel C A.An introduction to Homological algebra[M].Cambridge:Cambridge University Press,1994:104-119.