Homological Methods in Local Algebra

Termine und Zeiten:

Vorlesungen: Montag, 16-18 ct, Raum B 039.
Übungen: Dienstag, 12-14 ct, Raum B 039.

Zusammenfassung:

One of the first famous applications of methods of homological algebra was the proof by Auslander–Buchsbaum and Serre of the conjectures on the factoriality of regular local rings and on the regularity of their localizations, which have now become classical results [1–4]. Since then, methods of homological algebra have become an integral part of commutative algebra and algebraic geometry.

In the course we will start with the very basics of homological algebra, then discuss global dimension, Koszul complex, and homological characterization of regular rings following [4–7]. Then we will prove mentioned results about localizations and factoriality. If time permits, we will also discuss Cohen–Macaulay modules and depth, or K-theory of regular rings.

Voraussetzung:

This course will be of interest to Master students majoring in Algebra. I will assume that the students are familiar with Algebra I & II courses. Knowledge of Algebraic Geometry is not strictly required, but will be helpful. The course will be taught in English.

Klausur:

The exam will take place on Tuesday 16 July from 12:15 until 14:00 in room B 039. No materials are permitted in the exam. Please ensure you bring with you an appropriate identity document with photo.
If you are considering taking the exam, please register by sending me a short email with your name and Matrikelnr.
Solutions to the exam
Results of the exam
Klausureinsicht will take place on Wednesday, July 17th from 15:00 until 15:45 in my office B427. Please write me an e-mail to confirm an appointment.