Generators and representability of functors in commutative and noncommutative geometry

Details Generators and representability of functors in commutative and noncommutative geometry Generators and representability of functors in commutative and noncommutative geometry

2002-04-17

arxiv.org/abs/math/0204218v2

Mathematics

Algebraic Geometry

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Scientific paper

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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