Seminar in homological algebra
Masters Seminar in Homological Algebra
This is a seminar in the foundations of homological algebra, with applications to commutative algebra. We will introduce such basic notions as triangulated categories, Verdier localization and dervied functors, with examples furnished by the homotopy category of complexes and the derived category of an abelian category. We will look at the homological algebra of modules over a ring, discussing Tor and Ext and using these tools to derive results in commutative algebra, such as the homological characterization of regular local rings. For more details as to the topics and sources, please see the Seminar Program. For details as to the individual lectures, see the Lecture Program
The seminar meets Fridays, 14-16 Uhr in WSC-S-U-3.03
Lecture 1. 20.04-Jonas Franzel. Ab-categories, additive categories, abelian categories and the category of complexes
Lecture 2. 27.04-Paulina Fust. The homotopy category of complexes
Lecture 3. 04.05-Francesco Chiatti. Homology and cohomology
Lecture 4. 11.05-Florian Leptien. Triangulated categories
Lecture 5 18.05-Fangzhou Jin. Verdier localization and the derived category
Lecture 6 18.05-Francesco Chiatti. Computations in the derived category: injective and projective resolutions
Lecture 7 01.06-Jonas Franzel. Derived functors and $\delta$-functors
Lecture 8 15.06-Florian Leptien. Examples of derived functors and (co)homolgoical functors
Lecture 9 22.06-Paulina Fust. Spectral sequences
Lecture 10 29.06-N.N.
Lecture 11 06.07-N.N.
Lecture 12 13.07-N.N.
Lecture 13 20.07-N.N.