On compact generation of deformed schemes. (English) Zbl 1345.14023
Summary: 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.
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 14D15 | Formal methods and deformations in algebraic geometry |
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