A representation-theoretic approach to recollements of abelian categories
A representation-theoretic approach to recollements of abelian categories
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DOI：
10.1090/conm/716/14427
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Chrysostomos Psaroudakis
中科院分区：
文献类型：
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作者：
Chrysostomos Psaroudakis
回忆情形是由Beilinson，Bernstein和Deligne在他们关于倒叶的开创性论文中，在三角范畴的背景下引入的。这主要是一篇关于阿贝尔范畴的回忆的综述论文，重点是表象理论的应用。这篇文章的很大一部分内容是关于交换范畴回集的结构和同调结果。我们的目的是在阿贝尔范畴的背景下统一处理回忆论，并给出在Artin代数的表示论中的几个应用。我们还包括与豪尔赫·维托里亚在相容扭转对和心脏记忆方面的未发表工作。
Recollement situations were introduced by Beilinson, Bernstein and Deligne in the context of triangulated categories in their seminal paper on perverse sheaves. This is mainly a survey paper on recollements of abelian categories with emphasis on representation-theoretic applications. A large part of the paper is devoted to structural and homological results of recollements of abelian categories. Our aim is to present a unified treatment of the theory of recollements in the context of abelian categories and present several applications in Representation Theory of Artin Algebras. We also include unpublished work with Jorge Vitória on compatible torsion pairs and recollements of hearts.