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Presheaves of triangulated categories and reconstruction of schemes

โœ Scribed by P. Balmer

Publisher
Springer
Year
2002
Tongue
English
Weight
179 KB
Volume
324
Category
Article
ISSN
0025-5831

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๐Ÿ“œ SIMILAR VOLUMES

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We show that the idempotent completion of a triangulated category has a natural structure of a triangulated category. The idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion. In particular, the derived category of an idem

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It is a pleasure to thank Mark Hovey for the proof of Lemmas 3.6 and other help and to thank Halvard Fausk, John Greenlees, and Gaunce Lewis for careful reading and helpful comments.

Relations for the Grothendieck groups of
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โœ Jie Xiao; Bin Zhu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 132 KB

A class of triangulated categories with a finiteness condition is singled out. These triangulated categories have Auslander-Reiten triangles. It is proved that the relations of the Grothendieck group of a triangulated category in this class are generated by all Auslander-Reiten triangles. Moreover,