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

Daniel Murfet

Number | 53 |
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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.