#### Fall 2017

# MA3204 Homological algebra

### Lecturer

**Torkil Utvik Stai** (torkil.stai[at]math.ntnu.no)

### Lectures

- Tuesday 10-12, room 656
- Thursday 12-14, room 734

### Exercises

### Content

A detailed list of subjects discussed in this course in 2013 can be found here. The plan is to cover approximately the same content this year.

**From the study hand book:**

The course deals with homological algebra for abelian categories in general, and modules over a ring in particular.

First category theory is introduced, both in the setup of categories in general and abelian categories in particular, and some basic properties are discussed (functors, natural transformations, limits and colimits, in particular kernels, cokernels, pullbacks, pushouts).

The main part of the course focuses on the study of derived functors, in particular the derived functors Ext and Tor. To this end, the concepts of complexes, homotopy, homology, projective and injective resolutions are introduced and studied. The discussion of the first Ext also involves comparison to short exact sequences (Yoneda-Ext).

Finally triangulated, and in particular derived categories are introduced, and Ext is interpreted as morphism set in the derived category.

### Resources

The content of the course is what will be presented during lectures. We will mostly follow the notes of Steffen Oppermann. Please be aware that these likely contain typos and or mistakes. If you would like to have a book, the following can be used.

**Joseph J. Rotman**,*An introduction to Homological Algebra*, first edition**Joseph J. Rotman**,*An introduction to Homological Algebra*, second edition**Charles A. Weibel**,*An introduction to Homological Algebra*