### Lecture timetable

Mon 16:00 in MA B1.01 from Mon 8th Jan 2024
Thu 14:00 in MA B1.01
Fri 10:00 in MA B3.01
Support class: Fri 14:00 in B3.01 from Fri 19th Jan 2024
with TA Marc Truter <Marc.Truter@warwick.ac.uk>

### Partial lecture notes 2024

Crib-sheet "Frequently Forgotten Facts"

2024 overall syllabus

2024 Lecture 1
Dedekind and Weber 1882

Chap 5 of course notes, Weeks 6-8

Chap 6 of course notes, Weeks 9-10

David Rees' 1956 paper on the Hauptidealsatz

Appendix: Overview of homological algebra

Appendix on injective modules

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

Chapter 5: Koszul complex, regular sequence

Chapter 6: Depth, Cohen-Macaulay and Gorenstein

Appendix on Homological Algebra

### 2024 Worksheets

Worksheet_0 on prerequisites

Worksheet_1 Assignment deadline Mon 29th Jan at 12:00

Worksheet_2 Assignment deadline Mon 12th Feb at 12:00

Worksheet_3 Assignment deadline Mon 11th Mar at 12:00

Worksheet_4 Assignment deadline Mon 25th Mar at 12:00

### Write-up of Autumn 2022 lectures by Alexandros Groutides

Chapter 5 Regular sequences, the Koszul complex and regular local rings

Chapter 6 Cohen-Macaulay and Gorenstein rings

Chapter 7 Appendix on homological algebra

### Lecture notes from Autumn 2022

Week1

Week2

Week3

Weeks4-5

Week6
Lecture 17 Part I
Lecture 17 Part II
Lecture 18 Part I
Lecture 18 Part II

Here is the
Warwick UG Handbook entry.

### Lecture capture

To catch up on missed lectures (a few hours after they happen)

click on the Echo 360 Lecture Capture block on the right

of this
Moodle page

### Last year's notes

The information below refers to the course given in 2021-22.
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

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

Assessed questions from Example sheet 2

Example sheet 3

Example sheet 4

### Additional resources

Download
Marco Schlichting's 2013 notes