Generators and representability of functors in commutative and noncommutative geometry

  title={Generators and representability of functors in commutative and noncommutative geometry},
  author={Alexei Bondal and Michel van den Bergh},
  journal={arXiv: Algebraic Geometry},
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… 

Representability and autoequivalence groups

  • Xiao-Wu Chen
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2021
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