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Realisation Functors in Tilting Theory, Part II: Recollements of Derived Categories

作者:   来源:  时间:2015-09-22

  题目:Realisation Functors in Tilting Theory, Part II: Recollements of Derived Categories

  报告人: Dr. Chrysostomos Psaroudakis(Norway University of Scinces and Technology,Tronheim, Norway)

  摘要: Recollements of abelian, resp. triangulated, categories are exact sequences of abelian, resp. triangulated, categories where the inclusion functor as well as the quotient functor have left and right adjoints. They appear quite naturally in various settings and are omnipresent in representation theory. Recollements which all involved are module categories (abelian case) or derived categories of module categories (triangulated case) are of particular interest. In the abelian case, the "standard" example is the recollement induced by the module category of a ring R with an idempotent element e, and in the triangulated case the "standard" example is given as the derived counterpart of the previous recollement of module categories when the ideal ReR is stratifying. The latter recollement is called stratifying. In a recent work with Jorge Vitoria (2014), we showed that a recollement whose terms are module categories is equivalent to a recollement induced by the module category of aring with an idempotent element. Hence, in the abelian case all recollements of module categories are well understood. This is not the case for recollements of derived categories, even in the case where all of them are derived module categories. A natural question is whether every recollement of derived categories is equivalent to a derived version of a recollement of abelian categories. In this part, we use the realisation functors from Part I to provide a criteria for such an equivalence to exist. In particular, we provide necessary and sufficient conditions for a recollement of derived categories of module categories over rings to be equivalent with a stratifying one. As an application we show that this always holds in the case of finite dimensional hereditary algebras. This is joint work with Jorge Vitoria.

  时间:9月22日(周二)下午14:00-15:30

  地点:首都师大北二区教学楼 132 教室

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