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Auslander orders over nodal stacky curves and partially wrapped Fukaya categories

Research output: Contribution to journalArticle

Yanki Lekili, Alexander Polishchuk

Original languageEnglish
Pages (from-to)615-644
JournalJournal of Topology
Volume11
Issue number3
Early online date19 Jun 2018
DOIs
Accepted/In press14 Mar 2018
E-pub ahead of print19 Jun 2018
PublishedSep 2018

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  • Auslander orders over nodal_LEKILI_Accepted14March2018_GREEN AAM

    Auslander_orders_over_nodal_LEKILI_Accepted14March2018_GREEN_AAM.pdf, 487 KB, application/pdf

    Uploaded date:04 Apr 2018

    Version:Accepted author manuscript

    "This is the peer reviewed version of the following article: Lekili, Y. and Polishchuk, A. (2018), Auslander orders over nodal stacky curves and partially wrapped Fukaya categories. Journal of Topology, 11: 615-644, which has been published in final form at https://doi.org/10.1112/topo.12064. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions."

King's Authors

Abstract

Abstract
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.

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