2010/10/31 by Alberto Canonaco, Paolo Stellari
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Exact functor #Functor #Functor category #Homotopy and Cohomology in Algebraic Topology #Mathematics #Projective test #Pure mathematics #Type (biology) #math.AG
paper · pdf · doi:10.1112/s0010437x13007872
36 pages. Major revision and new results added. Accepted for publication in Compositio Math
arxiv created 2013/12/06 · openalex publication_date 2014/06/30 · arxiv updated 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We prove that exact functors between the categories of perfect complexes supported on projective schemes are of Fourier–Mukai type if the functor satisfies a condition weaker than being fully faithful. We also get generalizations of the results in the literature in the case without support conditions. Some applications are discussed and, along the way, we prove that the category of perfect supported complexes has a strongly unique enhancement.