# 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

## Schedule

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.