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Gluing semi-orthogonal decompositions

Scherotzke, Sarah, Sibilla, Nicolo, Talpo, Mattia (2020) Gluing semi-orthogonal decompositions. Journal of Algebra, 559 . pp. 1-32. ISSN 0021-8693. (doi:10.1016/j.jalgebra.2020.03.022) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:81712)

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https://doi.org/10.1016/j.jalgebra.2020.03.022

Abstract

We introduce preordered semi-orthogonal decompositions (psod-s) of dg-categories. We show that homotopy limits of dg-categories equipped with compatible psod-s carry a natural psod. This gives a way to glue semi-orthogonal decompositions along faithfully flat covers, extending the main result of [4]. As applications we will construct semi-orthogonal decompositions for root stacks of log pairs where D is a (not necessarily simple) normal crossing divisor, generalizing results from [17] and [3]. Further we will compute the Kummer flat K-theory of general log pairs , generalizing earlier results of Hagihara and Nizioł in the simple normal crossing case [15], [23].

Item Type: Article
DOI/Identification number: 10.1016/j.jalgebra.2020.03.022
Uncontrolled keywords: Semi-orthogonal decompositions, Root stacks, Logarithmic geometry, Kummer flat K-theory
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Nicolo Sibilla
Date Deposited: 15 Jun 2020 10:04 UTC
Last Modified: 04 Mar 2024 19:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81712 (The current URI for this page, for reference purposes)

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