This is a course of 30 advanced lectures I gave online in 2021 during
the pandemic.
The lectures are far from perfect, but this is the
kind of thing that we were
able to do during the long Covid
lock-down, and some people have found
them useful since. The
material is mostly cribbed from Jean-Pierre Serre's
famous paper
cited below, with a considerable number of errors of my own invention.
The Warwick Math MA940 course description webpage is
here.
A brief and jokey summary of the content, is given in Chapter B
of my Park City lectures.
Videos of lectures
Lecture 1 Mon 11th Jan 2021
Lecture 2 Wed 13th
Lecture 3 Fri 15th
Lecture 4 Mon 18th
Lecture 5 Thu 21th
Lecture 6 Fri 22nd
Lecture 7 Mon 25th
Lecture 8 Thu 28th
Lecture 9 Fri 29th
Lecture 10 Mon 1st Feb
Lecture 11 Thu 4th
Lecture 12 Fri 5th
Lecture 13 Mon 8th
Lecture 14 Thu 11th
Lecture 15 Fri 12th
Lecture 16 Mon 15th
Lecture 17 Thu 18th
Lecture 18 Fri 19th
Lecture 19 Mon 22nd
Lecture 20 Thu 25th
Lecture 21 Fri 26th
Lecture 22 Mon 1st Mar
Lecture 23 Thu 4th
Lecture 24 Fri 5th
Lecture 25 Mon 8th
Lecture 26 Thu 11th
Lecture 27 Fri 12th
Lecture 28 Mon 15th
Lecture 29 Thu 18th
Lecture 30 Fri 19th
References
0.1. Serre Faisceaux Algebriques Coherents.pdf
0.2. Borel Serre Le théorème de Riemann-Roch.pdf
0.3. Alexander Grothendieck La théorie des classes de Chern.pdf
0.4. Park City, Chapter B.pdf
1.0.index.html
1.1. Notes_on_FAC.txt
1.2. MA940.txt
1.3. Contents.txt
1.4. injectives.txt
1.5. Exc sheet 1 (tentative).txt
index.html
Link_to_video_files
J.-P. Serre, Faisceaux algébriques cohérents, Ann. of Math.
61 (1955)
[FAC]
There is an English translation here:
https://achinger.impan.pl/fac/fac.pdf
A. Borel and J.-P. Serre, Le théorème de Riemann-Roch, Bull.
Soc. Math. France 86 (1958) 97--136
I.R. Shafarevich, Basic algebraic geometry I, Springer, 1994
R. Hartshorne, Algebraic geometry, Springer Graduate Texts, 1977
H. Matsumura, Commutative ring theory, CUP
Exercise sheets:
Please also look through the exercise sections in Hartshorne Chap. II.
Ex Sheet 1 (tentative)
Injective modules:
Existence of injective embeddings