A recollement construction of Gorenstein derived categories

doi:10.1007/s11464-018-0703-2

Front. Math. China

2018, Vol. 13

Issue (3) : 691-713 https://doi.org/10.1007/s11464-018-0703-2

RESEARCH ARTICLE

A recollement construction of Gorenstein derived categories

Peng YU(

)

Department of Elementary Education, Changsha Normal University, Changsha 410100, China

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Abstract

We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.

Keywords Recollements functor categories derived categories Gorenstein algebras weak excellent extension locally finitely presented categories

Corresponding Author(s): Peng YU

Issue Date: 11 June 2018

Cite this article:

Peng YU. A recollement construction of Gorenstein derived categories[J]. Front. Math. China, 2018, 13(3): 691-713.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0703-2
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I3/691

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