Local to global principles for generation time over commutative Noetherian rings (Q2240610)

\textit{A. Bondal} and \textit{M. van den Bergh} [Mosc. Math. J. 3, No. 1, 1--36 (2003; Zbl 1135.18302)] introduced the notion of generation of a complex \(G\) in the derived category of a commutative Noetherian ring. Similarly, the level of an object in triangulated category was introduced in [\textit{L. L. Avramov} et al., Adv. Math. 223, No. 5, 1731--1781 (2010; Zbl 1186.13006)]. In this paper, the author studied the local to global principle for these invariants by a key lemma of [\textit{S. Oppermann} and \textit{J. Št'ovíček}, Bull. Lond. Math. Soc. 44, No. 2, 285--298 (2012; Zbl 1244.18010)]. For a commutative Noetherian ring \(R\), the main results of this paper show that the level of object in derived category of \(R\) and the upper bound of generation time have the local to global property.