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ID:39132487
大小:860.91 KB
页数:33页
时间:2019-06-25
《广义局部上同调模》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、广义局部上同调模摘要局部上同调理论最早是由Grothendieck定义的,在之后的数学研究中得到肯定并成为研究交换代数和代数几何的一个有效工具.1974年,Herzog对局部上同调理沦进行推广,给出了广义局部上同凋模的概念.本文就是在此基础上研究了广义局部上同调模郇(^,,N)的■弱上有限性和L弱余上有限性,还有Ext失(R/I,研(』I,,Ⅳ))的弱余拉斯克性.本文在[1】的基础上做了进一步探索.共分为四章,主要内容如下:第一章,预备知识,介绍了一些与广义局部上同调模相关的概念、基本结论和基本定理,为我们下一步的研究课题做准备.第二章,在已知弱拉斯克模和L弱上有限等概念的基础上
2、,研究了广义局部上同调模的Artin性和,.弱上有限
3、生,在JI,有限生成,日}(Ⅳ)(对于Vi4、Vi5、eometry.Inl974,J.Herzogintroducedthenotationofgeneralizedlocalcohomologywithrespecttoapairofmodules.Inthisarticle,westudytheI-weaklycofinitenessandI-weaklyCO-cofinitenessofgeneralizedlocalcohomologymodule研(^,,N).Inaddition,westudytheweaklyco-laskerianpropertyofmoduleExth(R/I,研(尬Ⅳ)).Themaincon6、tentofthepaperisthefollowing:Inchapter1,werecallsomebasicconceptsandpreliminaryresultsaboutgenevalizedlocalcohomology,whichwillbeprobablyusedinthispaper.Inchapter2.wegivethedefinitionsoftheW.LmoduleandI-weaklycofinite-ness.Then,westudytheArtiniannessandLweaklycofinitenessofgeneralizedlocalcoh7、omologymodules,andgivesomesufficientconditions.WhenMisfinitelygener-ated,and研(Ⅳ)(i8、lcohomologymodules,andgivesomesufficientconditions.WhenMisfinitelygenerated,and研(Ⅳ)(i
4、Vi5、eometry.Inl974,J.Herzogintroducedthenotationofgeneralizedlocalcohomologywithrespecttoapairofmodules.Inthisarticle,westudytheI-weaklycofinitenessandI-weaklyCO-cofinitenessofgeneralizedlocalcohomologymodule研(^,,N).Inaddition,westudytheweaklyco-laskerianpropertyofmoduleExth(R/I,研(尬Ⅳ)).Themaincon6、tentofthepaperisthefollowing:Inchapter1,werecallsomebasicconceptsandpreliminaryresultsaboutgenevalizedlocalcohomology,whichwillbeprobablyusedinthispaper.Inchapter2.wegivethedefinitionsoftheW.LmoduleandI-weaklycofinite-ness.Then,westudytheArtiniannessandLweaklycofinitenessofgeneralizedlocalcoh7、omologymodules,andgivesomesufficientconditions.WhenMisfinitelygener-ated,and研(Ⅳ)(i8、lcohomologymodules,andgivesomesufficientconditions.WhenMisfinitelygenerated,and研(Ⅳ)(i
5、eometry.Inl974,J.Herzogintroducedthenotationofgeneralizedlocalcohomologywithrespecttoapairofmodules.Inthisarticle,westudytheI-weaklycofinitenessandI-weaklyCO-cofinitenessofgeneralizedlocalcohomologymodule研(^,,N).Inaddition,westudytheweaklyco-laskerianpropertyofmoduleExth(R/I,研(尬Ⅳ)).Themaincon
6、tentofthepaperisthefollowing:Inchapter1,werecallsomebasicconceptsandpreliminaryresultsaboutgenevalizedlocalcohomology,whichwillbeprobablyusedinthispaper.Inchapter2.wegivethedefinitionsoftheW.LmoduleandI-weaklycofinite-ness.Then,westudytheArtiniannessandLweaklycofinitenessofgeneralizedlocalcoh
7、omologymodules,andgivesomesufficientconditions.WhenMisfinitelygener-ated,and研(Ⅳ)(i8、lcohomologymodules,andgivesomesufficientconditions.WhenMisfinitelygenerated,and研(Ⅳ)(i
8、lcohomologymodules,andgivesomesufficientconditions.WhenMisfinitelygenerated,and研(Ⅳ)(i
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