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arXiv · 1901.01257

Gluing semi-orthogonal decompositions

Sarah Scherotzke·Nicolò Sibilla·Mattia Talpo
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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 some results of [4]. As applications we will construct semi-orthogonal decompositions for root stacks of log pairs (X,D) where D is a (not necessarily simple) normal crossing divisors, generalizing results from [17] and [3]. Further we will compute the Kummer flat K-theory of general log pairs (X,D), generalizing earlier results of Hagihara and Nizio{\l} in the simple normal crossing case [15], [23].

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Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo. 2019-01-04. Gluing semi-orthogonal decompositions. https://doi.org/10.1016/j.jalgebra.2020.03.022

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