Generators and representability of functors in commutative and noncommutative geometry
Algebraic Geometry
2007-05-23 v2 Category Theory
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.
Cite
@article{arxiv.math/0204218,
title = {Generators and representability of functors in commutative and noncommutative geometry},
author = {Alexei Bondal and Michel Van den Bergh},
journal= {arXiv preprint arXiv:math/0204218},
year = {2007}
}
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