Dhyan Aranha's seminar/exam

[Emanuele Tuillier Illingworth]

Dhyan Aranha will speak on "Homological methods in commutative
algebra" on Friday December 18th at 10:30 in room 136. This is a
seminar/exam for the course "Commutative Algebra".

Abstract: In this talk I want to discuss how one can use
results/methods from homological algebra to prove the
Auslander-Buchsbaum formula: pd_R (M) + depth(M) = depth(R), where R
is a Noetherian local ring, M is a nonzero finitely generated R-module
and pd_R(M) is finite. If there is time (there should be!) I would
like to sketch a proof of Serre's criterion for a Noetherian local
ring to be regular. I will assume familiarity with Ext and Tor
functors.