Local to global principles for generation time over commutative noetherian rings

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.

Keywords

local to global principle, generation time, level, coghost

2010 Mathematics Subject Classification

Primary 18E30. Secondary 13B30, 16E35.

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Partly supported by the NSF grant DMS-1700985, and the Alexander von Humboldt Foundation in the framework of an Alexander von Humboldt Professorship endowed by the German Federal Ministry of Education and Research.

Received 18 September 2019

Received revised 16 October 2020

Accepted 31 October 2020

Published 3 November 2021