Derived categories III
Topics for the third course. Here is a tentative list of topics – the actual choice of topics will be influenced by the participants. Some of the material will be taken from textbooks, and some from research papers. There will be a few guest lectures.
- Derived categories in commutative algebra: dualizing complexes, affine Grothendieck duality, local duality, rigid dualizing complexes.
- Derived categories in algebraic geometry: derived direct and inverse image functors, rigid residue complexes, global Grothendieck duality, applications to birational geometry (survey), perverse sheaves (survey), l-adic cohomology and Poicaré-Verdier duality (survey).
- Derived categories in noncommutative ring theory: dualizing complexes, tilting complexes, the derived Picard group, derived Morita theory.
- Derived algebraic geometry (survey): nonlinear derived categories, infinity categories, derived algebraic stacks, applications to mathematical physics.
The lectures will be in English.