Descending strong generation in algebraic geometry
Abstract
We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications we show that strong generation for the singularity category of a Noetherian separated scheme is Zariski local and obtain a strong generation result for the bounded derived category of a Noetherian concentrated algebraic stacks with finite diagonal.
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