MA4J8 Commutative Algebra II

Here is the Warwick UG Handbook entry.

Lecture timetable

Mon 15:00 in MS.02
Tue 12:00 in MS.01
Fri 17:00 in MS.01

Teaching assistant Patience Ablett <Patience.Ablett@warwick.ac.uk>
Support class Fri 15:00 in MS.02

Lecture capture

I request that those attending the live lectures wear a face mask and
keep a distance from me.   The lectures are live-streamed and captured
for those unable to attend in person:   click on the Echo 360 Lecture Capture
block on the right of this Moodle page

Some 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
Lect 7-8 Introduction to completion. Hensel's Lemma
Lect 9-10 Formal treatment of completion. Artin-Rees lemma and exactness of I-adic completion
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

Homework sheets

There will be 4 Assessed worksheets, with submission deadlines 12:00 noon on
   Week 3 Fri 22nd Oct
   Week 5 Fri 12th Nov
   Week 7 Fri 26th Nov
   Week 10 Fri 9th Dec
Example sheet 1    Questions 1,8 and 11 are assessed questions.
Solution to Q10
Example sheet 2 (first draft)
   Assessed questions from Example sheet 2

Additional resources

Download Marco Schlichting's 2013 notes