Recollements and stratifications of derived module categories

由Beilinson、伯恩斯坦和Deligne引入的复元概念允许解构导出模范畴。它可以被看作是一个短的正合序列的类似物，从而也提供了“简单”的派生范畴和派生模范畴的“分层”和“合成序列”的定义。该项目调查简单的派生类别，以及在这种情况下的乔丹持有人定理的有效性。它的目的是建立一个密切的联系与倾斜理论和应用同调和K理论的不变量。技术要进一步发展和应用涉及同调满态，普遍定位，近似和微分分次代数。

The concept of recollement, introduced by Beilinson, Bernstein and Deligne, allows to deconstruct derived module categories. It can be seen as an analogue of a short exact sequence, thus also providing definitions of ’simple’ derived categories and of ’stratifications’ and ’composition series’ of derived module categories. The project investigates simple derived categories as well as the validity of a Jordan-Holder theorem in this context. It aims at establishing a close connection with tilting theory and at applications to homological and K-theoretic invariants. Techniques to be developed further and to be applied involve homological epimorphisms, universal localisation, approximations and differential graded algebras.