Gluing semi-orthogonal decompositions
| Autor: | Mattia Talpo, Sarah Scherotzke, Nicolò Sibilla |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Kummer flat K-theory Logarithmic geometry Root stacks Semi-orthogonal decompositions Algebra and Number Theory Homotopy Carry (arithmetic) 010102 general mathematics Divisor (algebraic geometry) 01 natural sciences Mathematics - Algebraic Geometry Simple (abstract algebra) 0103 physical sciences FOS: Mathematics 14F05 19E08 Mathematics [G03] [Physical chemical mathematical & earth Sciences] 010307 mathematical physics Settore MAT/03 - Geometria Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] 0101 mathematics QA Algebraic Geometry (math.AG) Mathematics |
| ISSN: | 0021-8693 |
| Popis: | 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]. Comment: v2: implemented referee's advice. Partially formerly part of arXiv:1803.06398 |
| Databáze: | OpenAIRE |
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