Smooth and proper noncommutative schemes and gluing of dg categories
type: Item
instance of: scholarly article
title: Smooth and proper noncommutative schemes and gluing of dg categories
zbMATH Open document ID: 1368.14031
published in: Advances in Mathematics
publication date: 2016-09-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1402.7364
review text: The author defines noncommutative schemes to be dg-categories satisfying some additional properties. Properties such that compactness, smoothness, and properness are extended to noncommutative schemes. One big class of examples is provided by certain subcategories of perfect complexes on smooth projective schemes. Furthermore, a gluing operation for noncommutative schemes is defined via bimodules of dg-categories. From these a number of results are shown about finite-dimensional algebras and noncommutative projective planes.
reviewed by: John Zhang
Mathematics Subject Classification ID: 14A30
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 16E45
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 14F08
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 6631654
zbMATH Keywords: differential graded categories
zbMATH Keywords: triangulated categories
zbMATH Keywords: noncommutative schemes
zbMATH Keywords: noncommutative geometry
zbMATH Keywords: perfect complexes
author: Dmitri Orlov
MaRDI profile type: Publication
OpenAlex ID: W2098015562
arXiv ID: 1402.7364
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DOI: 10.1016/J.AIM.2016.07.014
description: scientific article; zbMATH DE number 6631654