Recollements and stratifications of derived module categories

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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.