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arXiv · 0904.2685

Rouquier's cocovering theorem and well-generated triangulated categories

Daniel Murfet
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Abstract

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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Daniel Murfet. 2009-04-17. Rouquier's cocovering theorem and well-generated triangulated categories. https://arxiv.org/abs/0904.2685

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