2022/12/13 by Mirko Mauri, Evgeny Shinder, Mauri, Mirko +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2212.06786
openalex publication_date 2022/12/13 · openalex created_date 2022/12/27 · openalex updated_date 2026/07/28
Given a resolution of rational singularities π\colon X → X over a field of characteristic zero we use a Hodge-theoretic argument to prove that the image of the functor Rπ_*\colon D(X) → D(X) between bounded derived categories of coherent sheaves generates D(X) as a triangulated category. This gives a weak version of the Bondal-Orlov localization conjecture, answering a question of Pavic and Shinder. The same result is established more generally for proper (non-necessarily birational) morphisms π\colon X → X, with X smooth, satisfying Rπ_*(O_X) = OX.