2011/03/16 by Alexey Elagin, Alexei D Elagin · 1 citation
Mathematics · #Action (physics) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Base (topology) #Base change #Category theory #Closed category #Corollary #Derived category #Descent (aeronautics) #Enriched category #Equivariant map #Functor #Geography #Group (periodic table) #Group action #Group theory #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Mathematical analysis #Mathematics #Model category #Morphism #Pure mathematics #Reductive group #Scheme (mathematics) #Statistics #Variety (cybernetics) #math.AG
paper · pdf · doi:10.1070/sm2011v202n04abeh004153
published as Sbornik: Mathematics, 202:4 (2011), 495-526; Matematicheskiy Sbornik, 202:4 (2011), 31-64 (in Russian) · 28 pages
arxiv created 2011/03/16 · openalex publication_date 2011/04/30 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, we show that for an action of a reductive group on a scheme, the derived category of equivariant sheaves is equivalent to the category of objects, equipped with an action of the group, in the ordinary derived category.