Prerequisites:
We will assume familiarity with the language of schemes, for example corresponding to
part C: Introduction to Schemes or chapters II and III of Hartshorne's book
Algebraic Geometry.
Schedule:
We will have two talks of about one hour per week
(Tuesdays 15:3016:30 and Fridays 15:0016:00 UK time), and additionally will set aside some time to discuss exercises
(Tuesdays after talk).
Thanks to
Martin Gallauer for writing up a detailed programme for the first few weeks
here! (updated 12/07/21)
Topic 
Speaker 
Notes 
Exercises 
1. Introduction 
Martin G. 
Typed, Handwritten 
Problem set 1 
2. Étale morphisms 
Andrés, Håvard 
Typed 
Problem set 2 
3. Étale sheaves 
Martin O., Jay, Martin G. 
Typed, Slides 
Problem set 3 
4. Operations on sheaves 
Eduardo 
Typed 
Problem set 4 
5. Cohomology 
Lukas, George R. 
Slides, Typed 
Problem set 5 
6. First computations 
George C., Mike 
Slides, Typed 
Problem set 6 
7. Cohomology of curves 
Håvard, Andrés, Mike 
Typed 
PS 7, PS 8 
8. Proper & smooth base change 
Wojtek, Martin O. 
Slides 1, 2 
Problem set 9 
9. Finiteness theorems 
Martin G. 


10. Cohomological purity, cycle classes 
Andres, Eduardo 
Notes , notes 
Problem set 10 
11. Poincaré duality and Lefschetz trace formula 
Jay, Martin O. 


12. The Weil conjectures 
Håvard 

Problem set 11 
A PDF containing all the notes so far can be found
here. Comments, corrections and criticisms are most welcome!
Resources and references:
The main reference is Milne's book
Étale cohomology. Additionally, the following might be useful:
There are also many other websites for seminars on the same topic: