Rouquier's cocovering theorem and well-generated triangulated categories

Details Rouquier's cocovering theorem and well-generated triangulated categories Rouquier's cocovering theorem and well-generated triangulated categories

2009-04-17

arxiv.org/abs/0904.2685v1

Mathematics

Category Theory

18 pages, comments welcome

Scientific paper

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal $\alpha$ the condition of $\alpha$-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 $\alpha$-compact objects in the unbounded derived category of a quasi-compact semi-separated scheme.

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