Some adjoints in homotopy categories
type: Item
instance of: scholarly article
title: Some adjoints in homotopy categories
zbMATH Open document ID: 1205.18008
author: Amnon Neeman
published in: Annals of Mathematics. Second Series
publication date: 2010-05-27T00:00:00Z
full work available at URL: p16.xhtml
review text: Let \(R\) be a ring. Let \({\mathcal K}(R\text{-Flat})\) (\({\mathcal K}(R\text{-Proj})\)) denote the homotopy category of cochain complexes of flat, (respectively, projective) \(R\)-modules. In a previous paper [see Invent. Math. 174, No.~2, 255--308 (2008; Zbl 1184.18008)], the author proved that \({\mathcal K}(R\text{-Proj})\) is a Verdier quotient of \({\mathcal K}(R\text{-Flat})\). Let \(j^*:{\mathcal K}(R\text{-Flat})\to {\mathcal K}(R\text{-Proj})\) denote the quotient functor. The main theorem in the paper proves that \(j^*\) has a right adjoint \(j_*\). The author mentions that this theorem has a generalization to (non-affine) schemes.
reviewed by: Adrian Langer
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16B50
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 5712771
zbMATH Keywords: homotopy category
zbMATH Keywords: projective modules
zbMATH Keywords: flat modules
MaRDI profile type: Publication
OpenAlex ID: W2030459192
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DOI: 10.4007/ANNALS.2010.171.2143
description: scientific article; zbMATH DE number 5712771