MA4J8 Commutative Algebra II

Tue 11:00 MS.05 from Tue 4th Oct 2022
Thu 9:00 B3.03
Fri 15:00 A1.01
Support class Thu 16:00 in B1.01 from Thu 13th Oct 2022

Here is the Warwick UG Handbook entry.

Lecture capture

Last year's notes

Plans My initial plans for the course

Lect 1 What is commutative algebra? [Sorry, no lecture capture.]
Lect 2 Dedekind domain, Existence of primes [Sorry, I forgot to
wear the microphone for first 45 minutes.]
More on DVRs Further discussion and exercises on Discrete valuation rings.
Lect 3 First ideas on Spec A and the Zariski topology
Lect 4-5 Varieties versus Spec A. Chain conditions
Lect 6 Finite length modules. An Artinian ring is Noetherian
Lectures 7-10. Completion and Hensel's Lemma
Lect 12-14 Dimension theory. Graded rings and modules and their Hilbert series
Lect 15-17 Hilbert-Samuel functions and the main theorem of dimension theory
Lect 18-22 Syzygies and regular sequences
Lect 25-29 Ext and depth - preliminary draft

Homework sheets

   Week 3 Fri 22nd Oct
   Week 5 Fri 12th Nov
   Week 7 Fri 26th Nov
   Week 10 Fri 9th Dec

Additional resources