Rus

DG-categories

Lectures:

• Lecture 1 (17.09.2013). DG-algebras, DG-categories, and DG-functors.
• Lecture 2 (24.09.2013). DG-modules.
• Lecture 3 (01.10.2013). Trianguated structure on the homotopy category of DG-modules.
• Lecture 4 (08.10.2013). Derived category of DG-modules. Homotopically projective and injective DG-modules.
• Lecture 5 (15.10.2013). Perfect DG-modules, twisted complexes, tensor products.
• Lecture 6 (29.10.2013). Derived tensor product and RHom.
• Lecture 7 (05.11.2013). Drinfeld's quotient.
• Lecture 8 (12.11.2013). Drinfeld's quotient. Enhancements of derived categories.
• Lecture 9 (19.11.2013). H-injective and h-flat enhancements of the derived category of sheaves.
• Lecture 10 (26.11.2013). Properness and smoothness of DG-categories. Hochschild homology and cohomology.
• Lecture 11 (03.12.2013). Gluing of DG-categories. DG-categories of orbits.

Lecture notes:

• by Sveta Makarova: 1, 2, 3, 4, 5, 6, 7, 8, 9,
• by Igor Netay: 10,
• by Andrey Soldatenkov: 11.

• Examination program.
• Some problems (suggested by Sasha Efimov).

Literature:

• B. Keller. On differential graded categories
• B. Keller. Deriving DG categories
• V. Drinfeld. DG quotients of DG categories
• B. Toën. Lectures on DG categories
• B. Toën. The homotopy theory of dg-algebras and derived Morita theory
• B. Toën, M. Vaquié. Moduli of objects in dg-categories
• A. Bondal, M. Kapranov. Enhanced triangulated categories