科研之友
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摘要
Let (R, m, k) be a commutative noetherian local ring of Krull dimension d. We prove that the cohomology annihilator ca (R) of R contains a power of m if and only if, for some n >= 0, the nth syzygies in mod R are constructed from syzygies of k by taking direct sums/summands and a fixed number of extensions. These conditions yield that R is an isolated singularity such that the bounded derived category D-b (R) and the singularity category D-sg (R) have finite dimension, and the converse holds when R is Gorenstein. We also show that the modules locally free on the punctured spectrum are constructed from syzygies of finite length modules by taking direct sums/summands and d extensions. This result is exploited to investigate several ascent and descent problems between R and its completion (R) over cap.
- 出版日期2016-9
