2017/05/31 by Yankı Lekili, Yanki Lekili, Alexander Polishchuk · 36 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Analogy #Categorical variable #Derived category #Epistemology #Equivalence (formal languages) #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematics #Order (exchange) #Pure mathematics #math.AG #math.RT #math.SG
paper · pdf · doi:10.1112/topo.12064
published in Journal of Topology 11(3), 615-644 (Wiley) · 34 pages, 12 figures, accepted for publication by the Journal of Topology
arxiv created 2018/05/05 · openalex publication_date 2018/06/19 · arxiv updated 2018/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
It follows from the work of Burban and Drozd [Math. Ann. 351 (2011) 665–709] that for nodal curves C, the derived category of modules over the Auslander order A C provides a categorical (smooth and proper) resolution of the category of perfect complexes Perf ( C ) . On the A-side, it follows from the work of Haiden–Katzarkov–Kontsevich [Publ. Math. Inst. Hautes Études Sci. 126 (2017) 247–318] that for punctured surfaces X with stops Λ at their boundary, the partially wrapped Fukaya category W ( X , Λ ) provides a categorical (smooth and proper) resolution of the compact Fukaya category F ( X ) . Inspired by this analogy, we establish an equivalence between the derived category of modules over the Auslander orders over certain nodal stacky curves and partially wrapped Fukaya categories associated to punctured surfaces of arbitrary genus equipped with stops at their boundary. As an application, we deduce equivalences between derived categories of coherent sheaves (respectively perfect complexes) on such nodal stacky curves and the wrapped (respectively compact) Fukaya categories of punctured surfaces of arbitrary genus.