|
|
|
||
|
In the year 25/26 the course is aimed at derived Morita theory and homological techniques using differential
graded rings and small differential graded categories.
Last update: Šmíd Dalibor, Mgr., Ph.D. (13.10.2025)
|
|
||
|
The exam will be granted for a presentation of a project, which the student agrees on with the lecturer. Last update: Šmíd Dalibor, Mgr., Ph.D. (13.10.2025)
|
|
||
|
1) B. Keller, Deriving DG categories, Ann. Sci. École Norm. Sup. (4) 27 (1994), no. 1, 63-102.
2) B. Keller, Derived categories and tilting, Handbook of tilting theory, 49-104, London Math. Soc. Lecture Note Ser., 332, Cambridge Univ. Press, Cambridge, 2007.
3) J. Rickard, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), no. 3, 436-456.
4) M. Saorín, Dg algebras with enough idempotents, their dg modules and their derived categories, Algebra Discrete Math. 23 (2017), no. 1, 62-137. Last update: Šmíd Dalibor, Mgr., Ph.D. (13.10.2025)
|
|
||
|
Depends on the topic for the given year. Last update: Šmíd Dalibor, Mgr., Ph.D. (12.10.2025)
|
|
||
|
0. A short introduction to derived and triangulated categories.
1. Rickard's derived Morita theorem characterizing when two rings have equivalent derived categories.
2. A conceptual proof of Rickard's theorem was given by Keller using DG algebras.
3. DG categories, algebraic triangulated categories (as a solution to some known deficiencies of triangulated categories) and Keller's extension of the Morita theorem for them.
4. Pretriangulated dg categories as an (in principle more flexible) enhancement for triangulated categories. Last update: Šmíd Dalibor, Mgr., Ph.D. (13.10.2025)
|