241212 Categories of Sheaves (V) (WiSe 2014/2015)

Derived categories of sheaves have been studied since the sixties of the last century since they are the natural habitat of cohomology (=associate to a topological space an interesting graded module). It seemed long time a hopeless task to get explicit descriptions of these categories, but today there are special cases which we can understand using tilting theory. The aim of the lecture is to develop the theory far enough to study some examples in detail (projective spaces, Grassmannians, toric varieties, hypersurface singularities).

Requirements for participation, required level

The lecture is in english. We assume familliarity with algebraic structures (groups, rings, modules,..) and with basic concepts from homological algebra (categories, functors, adjoints,..). The lecture is in the intersection between homological algebra, algebraic geometry and representation theory of finite dimensional algebras, so any preknowledge here is useful but not required.