MA3204 Homological algebra
Om noen
- ikke har avtalt eksamenstidspunkt ennå,
- ikke husker tidspunktet som sto på liste, eller
- vil bytte tidspunkt
så send epost til meg (Steffen [dot] Oppermann [at] math [dot] ntnu [dot] no).
Timeplan
Forelesninger er
- Tirsdag, 16:15-18:00, i rom 734
- Fredag, 08:15-10:00, i rom 734
Øvinger
Content
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.
A more detailed list of subjects discussed in this course 2 years ago can be found here: contents (the plan is to cover approximately the same content this year)
Lecturer
Steffen Oppermann, room 844, Sentralbygg II, Steffen [dot] Oppermann [at] math [dot] ntnu [dot] no
Literature
The content of the course is what will presented during lectures. 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
I am also trying to provide some notes. Please be aware that these very likely contain many typos and or mistakes.
Referansegruppe
Vi hadde referansegruppemøte på 04.09., og de følgende punktene ble diskutert:
- Foreleseren er ugjennomsiktig, og burde være flinkere til å ikke stå foran det han akkurat har skrevet.
- Forelesningshastighet er akseptabelt.
- Øvinger: det kunne være med noen tilleggsoppgaver som er litt vanskeligere, slik at alle får noe de ikke klarer.