RESEARCH ARTICLE

A recollement construction of Gorenstein derived categories

  • Peng YU
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  • Department of Elementary Education, Changsha Normal University, Changsha 410100, China

Received date: 05 Jun 2016

Accepted date: 15 Apr 2018

Published date: 11 Jun 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

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.

Cite this article

Peng YU . A recollement construction of Gorenstein derived categories[J]. Frontiers of Mathematics in China, 2018 , 13(3) : 691 -713 . DOI: 10.1007/s11464-018-0703-2

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