Fall 2016

Prof Amnon Yekutieli

Course Content

Topics:

  1. Review of material from past semesters (the courses "Derived Categories I and II").

  2. Derived categories in commutative algebra: dualizing complexes, Grothendieck's local duality, MGM Equivalence, rigid dualizing complexes.

  3. Derived categories in algebraic geometry: direct and inverse image functors, global Grothendieck duality, applications to birational geometry (survey), -adic cohomology and Poincare-Verdier duality (survey), perverse sheaves (survey).

  4. Derived categories in non-commutative ring theory: dualizing complexes, tilting complexes, derived Morita theory.

  5. Derived algebraic geometry: nonabelian derived categories (survey), infinity categories (survey), derived algebraic stacks (survey), applications (survey).

Course Catalogue: 201.2.0363