当前位置: X-MOL 学术Bull. Iran. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the Cofiniteness of Small-Level Generalized Local Cohomology Modules
Bulletin of the Iranian Mathematical Society ( IF 0.7 ) Pub Date : 2019-08-29 , DOI: 10.1007/s41980-019-00287-3
Nguyen Van Hoang , Ngo Thi Ngoan

Let R be a commutative Noetherian ring and MN be two finitely generated R-modules. In this note, we prove the cofiniteness of generalized local cohomology modules \(H^{i}_{I}(M,N)\) with respect to I for all \(i<t\) and the finiteness of \((0:_{H^{t}_{I}(M,N)}I)\) provided \(H^{i}_{I}(M,N)_{\mathfrak {p}}\) is finitely generated for all \(i<t\) and all \(\mathfrak {p}\in \bigcup _{j<t}{{\,\mathrm{Supp}\,}}_{R}(H^{j}_{I}(M,N))\) with \(\dim R/\mathfrak {p}>1\), where t is a given non-negative integer. This extends the results of Bahmanpour and Naghipour (J Algebra 321:1997–2011, 2009), Bahmanpour et al. (Commun Algebra 41:2799–2814, 2013), and Cuong et al. (Kyoto J Math 55(1):169–185, 2015). This also provides a partially affirmative answer to Hartshorne’s question in Hartshorne (Invent Math 9:145–164, 1970) for the case of generalized local cohomology modules.

中文翻译:

小型广义局部同调模块的有限性

R为可交换的Noether环,而M,  N为两个有限生成的R-模。在本说明中,我们证明了对于所有\(i <t \)的广义局部同调模块\(H ^ {i} _ {I}(M,N)\)相对于I的有限性和\( (0:_ {H ^ {吨} _ {I}(M,N)} I)\)提供\(H ^ {I} _ {I}(M,N)_ {\ mathfrak {p}} \ )是为所有\(i <t \)和所有\(\ mathfrak {p} \ in \ bigcup _ {j <t} {{\,\ mathrm {Supp} \,}} _ {R}( H ^ {j} _ {I}(M,N))\)\(\ dim R / \ mathfrak {p}> 1 \),其中t是给定的非负整数。这扩展了Bahmanpour等人的研究结果(J Algebra 321:1997–2011,2009)。(Commun Algebra 41:2799–2814,2013),和Cuong等人。(Kyoto J Math 55(1):169-185,2015)。对于广义局部同调模块的情况,这也为Hartshorne在Hartshorne中提出的问题(Invent Math 9:145–164,1970)提供了部分肯定的答案。
更新日期:2019-08-29
down
wechat
bug