MA4J8 Commutative Algebra II

Mon 16:00 in MA B1.01 from Mon 6th Jan 2025
Thu 14:00 in MA B1.01
Fri 10:00 in MA B3.01
Support class: First session _Week 1_ Thu 9th Jan 13:00-14:00 in A1.01
with TA Marc Truter <Marc.Truter@warwick.ac.uk>

Example sheets

Partial lecture notes 2024

Alex Groutides' write-up of 2022-2023 lectures (with some new material)

2024 Worksheets

Write-up of Autumn 2022 lectures by Alexandros Groutides

Lecture notes from Autumn 2022

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