In the derived category of modules over a commutative noetherian ring a complex $G$ is said to generate a complex $X$ if the latter can be obtained from the former by taking summands and finitely many cones. The number of cones required in this process is the generation time of $X$. In this paper we present some local to global type results for computing this invariant, and discuss applications.

中文翻译：

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交换noetherian环上生成时间的局部到全局原则

在交换noetherian环上的模块的派生类别中，如果可以通过求和和有限个圆锥从前者获得复数$ X $，则称复数$ G $会生成复数$ X $。在此过程中所需的圆锥数是$ X $的生成时间。在本文中，我们提出了一些局部到全局类型的结果来计算该不变式，并讨论了其应用。