Course content

The course deals with central advanced concepts and methods in homological algebra, beyond what is covered in MA3204.

The contents of the course may vary from year to year. Usual topics include the following:

• Triangulated categories, in particular the derived category of a module category, and their properties.
• Enhancements of triangulated categories, typically to dg categories, model categories, or Frobenius categories, as well as what constructions these enhancements make possible that are not aloud in the underlying triangulated categories.
• Other types of categories (for instance exact categories, higher versions) may also be covered.

Other subjects may be taken up based on the interest of the lecturer and the participants.

Learning outcome

1. Knowledge. The student can provide definitions of key concepts, formulate and prove main results, and discuss examples of topics covered in the course..
2. Skills. The students can independently work in triangulated or exact categories, including employing standard techniques and searching relevant literature.
3. Competence. The students will be able to participate in scientific discussions, present results, and begin with research in homological algebra.

Learning methods and activities

The precise format of the course will vary, but it will require active student participation, including presentations.

The course will be taught as needed, subject to the availability of a teacher.

Recommended previous knowledge

MA3204 Homological algebra

Also MA3403 and MA3408 could be advantageous.

Course materials

Will be discussed at the start of the course.