Generators and representability of functors in commutative and noncommutative geometry

2002/04/17 by Alexei Bondal, Michel Van den Bergh, Bondal, Alexei +1 · 18 citations
Mathematics · #18E30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CT #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0204218

Minor changes

openalex publication_date 2002/04/17 · arxiv created 2002/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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