Advanced topics in algebra: Hochschild (co)homology


The goal of the course is to give an introduction to Hochschild (co)homology, focussing on its applications in deformation theory of algebras (and schemes), and the role of the Hochschild–Kostant–Rosenberg decomposition in all this. There will be three parts:

  1. Hochschild (co)homology for algebras
  2. Hochschild (co)homology and derived categories
  3. The Hochschild–Kostant–Rosenberg decomposition for schemes

The lecture notes are available. All comments are welcome!

There will be an oral exam.

Lectures are on Tuesday, from 10:15 to 11:45, and Wednesday, from 14:15 to 15:45, in N0.003. First lecture will be on April 10.


For the first part some basic knowledge of homological algebra is required, e.g. on the level of the first chapters of Weibel. For the second and third part we will need standard algebraic geometry, e.g. on the level of Hartshorne. Familiarity with derived categories will be helpful, but is not required. Daniel Huybrechts will be teaching a course on derived categories, which might be useful.


The first exam took place on July 24 and 25.

The exam takes place in Villa Maria, room 1.002. This is the building (which has number 62) next to the main building of the math department (which has number 60).

The second exam takes place on September 18. Please get in touch if I haven't already contacted you.

The schedule is as follows.

Julius Frank
Jan-Luca Spellmann
Jendrik Stelzner
Bjondina Kabashaj
Pedro Núñez
Fernando Abellan Garcia