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Generators and representability of functors in commutative and noncommutative geometry

Alexei Bondal·Michel Van den Bergh
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Abstract

We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence of a strong generator. We prove that the bounded derived categories of coherent sheaves on smooth proper commutative and noncommutative varieties have strong generators, hence saturated. In contrast the similar category for a smooth compact analytic surface with no curves is not saturated.

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Alexei Bondal, Michel Van den Bergh. 2002-07-17. Generators and representability of functors in commutative and noncommutative geometry. https://arxiv.org/abs/math/0204218

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