A recollement construction of Gorenstein derived categories

作     者：Peng YU 

作者机构：Department of Elementary Education Changsha Normal University Changsha 410100 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2018年第13卷第3期

页      面：691-713页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Acknowledgements The author would like to thank his supervisor Professor Zhaoyong Huang  for the valuable help  suggestions  guidance  and encouragement during his studies and preparation of this paper. He also thanks the referees for their careful reading and for pointing out related references. This work was partially supported by the National Natural Science Foundation of China (Grant No. 11571164) 

主　　题：Recollements functor categories derived categories Gorenstein algebras weak excellent extension locally finitely presented categories 

摘      要：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.