Homological algebra (seminar course) (2015/2016)

Course code
4S001439
Name of lecturer
Lidia Angeleri
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Period
I semestre dal Oct 1, 2015 al Jan 29, 2016.

Lesson timetable

I semestre
Day Time Type Place Note
Wednesday 1:30 PM - 3:30 PM lesson Lecture Hall M from Nov 4, 2015  to Jan 29, 2016

Learning outcomes

This reading course is devoted to some topics in homological algebra and representation theory.

Prerequisites: Representation Theory.

Syllabus

The first result we discuss states that the category of representations of the Kronecker algebra is derived equivalent to the category of coherent sheaves over the projective line.

We then study the construction of exact model structures together with the connections to cotorsion pairs and approximation theory. We discuss several applications, including the construction of monoidal model structures for the derived category of quasi-coherent sheaves of modules over a scheme. This part of the course is based on a paper by Jan Stovicek.

The last part of the course is devoted to an introduction to silting theory.

The reading course is complemented by some lecture series.
January 2016:
Discrete Derived Categories, by David Pauksztello, University of Manchester.
Aprile 2016:
Set theoretic methods in module theory, by Jan Trlifaj, Charles University Prague.
Model Theoretic and Functor Theoretic Methods in Representation Theory, by Mike Prest,University of Manchester.

More details are available on
http://profs.sci.univr.it/~angeleri/Homological algebra.html

Reference books
Author Title Publisher Year ISBN Note
W. Bruns; J. Herzog Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 39 Cambridge University Press 1998
E.Enochs, O.Jenda Relative homological algebra I De Gruyter 2000

Assessment methods and criteria

the students participate in the course and deliver a seminar talk.

STUDENT MODULE EVALUATION - 2015/2016