复形的局部上同调模的torsion函子OA北大核心
Torsion functors of local cohomology modules for complexes
证明了下有界复形的局部上同调模的torsion模属于Serre类,并且在某种情形下证明了复形的torsion模与局部上同调模的torsion模的同构式.作为此同构式的应用,我们用复形的局部上同调模表示了复形的Betti数.
We show that the torsion module TorRj(R/a,Hia(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism TorRs-t(R/a,X)≅ TorRs(R/a,Hta(X))in some case.As an application,the Betti number of a complex X in a prime ideal p can be computed by the Betti number of the local cohomology modules of X in p.
张平儿;马亚军
甘肃政法大学人工智能学院,甘肃 兰州 730070兰州交通大学数理学院,甘肃 兰州 730070
数理科学
局部上同调torsion函子Serre子范畴Betti数
local cohomologytorsion functorSerre subcategoryBetti number
《中山大学学报（自然科学版）（中英文）》 2025 (4)
109-114,6
Supported by Natural Science Foundation of Gansu Province(23JRRA866)Higher Education Innovation Fund of Gansu Provincial Department of Education(2025A-132)University-level Scientific Research and Innovation Project of Gansu University of Political Science and Law(GZF2024XQN16)Youth Foundation of Lanzhou Jiaotong University(2023023)
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