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2016•Arkiv för matematikOpen access

The dual of Brown representability for some derived categories

George Ciprian Modoi

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Abstract

Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB4∗-n category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely dimensional space.

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Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB4∗-n category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely dimensional space.

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Available abstract

Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB4∗-n category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely dimensional space.

Key concepts: Abelian category, Closed category, Biproduct, Mathematics, Category of groups, Dual (grammatical number), Derived category, Concrete category

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