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Rouquier's cocovering theorem and well-generated triangulated categories

Daniel Murfet

Number 53
Author Daniel Murfet
Project C01
Year 2009

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal α the condition of α-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was established for ordinary compactness by Rouquier. Our result yields a new technique for proving that a given triangulated category is well-generated. As an application we describe the α-compact objects in the unbounded derived category of a quasi-compact semi-separated scheme.

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