On the homotopy category of AC-injective complexes

doi:10.1007/s11464-016-0551-x

Front. Math. China

2017, Vol. 12

Issue (1) : 97-115 https://doi.org/10.1007/s11464-016-0551-x

RESEARCH ARTICLE

On the homotopy category of AC-injective complexes

James GILLESPIE(

)

Ramapo College of New Jersey, School of Theoretical and Applied Science, Mahwah, NJ 07430, USA

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Abstract

Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call AC-injective complexes, showing that K(AC-Inj), the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DGinjective complexes are AC-injective and in fact there is a recollement linking K(AC-Inj) to the usual derived category D(R). This is based on the author’s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.

Keywords AC-injective recollement compactly generated triangulated category

Corresponding Author(s): James GILLESPIE

Issue Date: 17 November 2016

Cite this article:

James GILLESPIE. On the homotopy category of AC-injective complexes[J]. Front. Math. China, 2017, 12(1): 97-115.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0551-x
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I1/97

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