Recollements and stratifications of derived module categories

由Beilinson， Bernstein和Deligne引入的概念允许解构派生的模块类别。它可以看作是短精确序列的类比，因此也提供了派生模块类别的“简单”衍生类别和“分层”和“组成系列”的定义。该项目研究了简单的派生范畴，以及在这种情况下约旦-霍尔德定理的有效性。它的目的是建立与倾斜理论的密切联系，以及在同调不变量和k理论不变量中的应用。有待进一步发展和应用的技术涉及同调上胚、普遍局域化、近似和微分梯度代数。

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.