Chrysostomos Psaroudakis

Recollements of Module Categories

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.

Realisation functors in tilting theory

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an injective cogenerator. For this purpose we develop a theory of (non-compact, or large) tilting and cotilting objects that generalises the preceding notions in the literature. Within the scope of derived Morita theory for rings we show that, under some assumptions, the realisation functor is a derived tensor product. This fact allows us to approach a problem by Rickard on the shape of derived equivalences. Finally, we apply the techniques of this new derived Morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t-structures glueing to a tilting or a cotilting t-structure. As a further application, we answer a question by Xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras.

Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements

Given an artin algebra

On Artin Algebras Arising from Morita Contexts

\Lambda

Ladders of Compactly Generated Triangulated Categories and Preprojective Algebras

with an idempotent element

Homological theory of recollements of abelian categories

a

Monomorphism Categories via Morita rings, Gorenstein algebras, AR sequences and derived equivalences

we compare the algebras

Derived invariance of support varieties

\Lambda

Infinite ladders induced by preprojective algebras

and

Reduction techniques for the finitistic dimension.

a\Lambda a