2024/02/07 by Alberto Canonaco, Canonaco, Alberto, Christian Haesemeyer +5 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2402.04605
openalex publication_date 2024/02/07 · openalex created_date 2024/02/09 · openalex updated_date 2026/07/28
In this article we prove that all the inclusions between the 'classical' and naturally defined full triangulated subcategories of a weakly approximable triangulated category are intrinsic (in one case under a technical condition). This extends all the existing results about subcategories of weakly approximable triangulated categories. Together with a forthcoming paper about uniqueness of enhancements, our result allows us to generalize a celebrated theorem by Rickard which asserts that if R and S are left coherent rings, then a derived equivalence of R and S is "independent of the decorations". That is, if D^?(R-\square) and D^?(S-\square) are equivalent as triangulated categories for some choice of decorations ? and \square, then they are equivalent for every choice of decorations. But our theorem is much more general, and applies also to quasi-compact and quasi-separated schemes -- even to the relative version, in which the derived categories consist of complexes with cohomology supported on a given closed subscheme with quasi-compact complement.