Seminar

Derived categories of coherent sheaves

Prof. Dr. LiedtkeProf. Dr. Viehmann, Prof. Dr. Rosenschon (LMU)

 

Time and place

  Tuesdays, 14:15 - 15:45 and 16:15 - 17:45 in MI 02.08.020

Contents

Associated to an Abelian category, we its category of bounded complexes, which - after identifying homotopies and inverting quasi-isomorphisms - yields the derived category. The derived category is the perfect framework for cohomology, derived functors, spectral sequences, Grothendieck-Verdier duality,...
Being algebraic geometers, we consider for a scheme the derived category of coherent modules. At first sight, this may seem like a rather abstract and technical object. However, in recent years it became clear that it is a useful object to study, that it captures important information, that it is (despite its appearance) a rather geometrical object, and that it also provides a beautiful framework for many results and conjectures.

Literature

  S. Gelfand, Y. Manin: Methods of Homological Algebra
D. Huybrechts: Fourier-Mukai Transforms in Algebraic Geometry

Detailed Program