On compact generation of deformed schemes

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• 作者：Wendy Lowen ; Michel Van den Bergh
• 关键词：Grothendieck category ; Derived category ; Compact generation ; Deformation ; Surface
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：10 September, 2013
• 年：2013
• 卷：244
• 期：Complete
• 页码：441-464
• 全文大小：282 K

文摘

We obtain a theorem which allows to prove compact generation of derived categories of Grothendieck categories, based upon certain coverings by localizations. This theorem follows from an application of Rouquier¡¯s cocovering theorem in the triangulated context, and it implies Neeman¡¯s result on compact generation of quasi-compact separated schemes. We prove an application of our theorem to non-commutative deformations of such schemes, based upon a change from Koszul complexes to Chevalley-Eilenberg complexes.