作者
Sean Sather-Wagstaff, Richard Wicklein
发表日期
2017/6/3
期刊
Communications in Algebra
卷号
45
期号
6
页码范围
2569-2592
出版商
Taylor & Francis
简介
Let X be a chain complex over a commutative noetherian ring R, that is, an object in the derived category 𝒟(R). We investigate the small support and co-support of X, introduced by Foxby and Benson, Iyengar, and Krause. We show that the derived functors and RHomR(M,−) can detect isomorphisms in 𝒟(R) between complexes with restrictions on their supports or co-supports. In particular, the derived local (co)homology functors RΓ𝔞(−) and LΛ𝔞(−) with respect to an ideal 𝔞⊊R have the same ability. Furthermore, we give reprove some results of Benson, Iyengar, and Krause in our setting, with more direct proofs. Also, we include some computations of co-supports, since this construction is still quite mysterious. Lastly, we investigate “𝔞-adically finite” R-complexes, that is, the X∈𝒟b(R) that are 𝔞-cofinite à la Hartshorne. For instance, we characterize these complexes in terms of a finiteness condition on LΛ𝔞(X).
学术搜索中的文章
S Sather-Wagstaff, R Wicklein - Communications in Algebra, 2017