Northwestern University, summer 2020

**Time:** Mondays 1:00pm-1:50pm, Thursdays 12:00pm-12:50pm.

**Location:** Zoom

**Remark:** We started on Thursday, July 2 and the final talk was on Thursday, September 10.

**Notes:**

- introduction - Viktor Burghardt
- étale morphisms - Adam Holeman
- Grothendieck topologies, sites and fpqc - Viktor Burghardt
- sheaf cohomology - Eivind Hjelle
- Čech cohomology - Eivind Hjelle
- descent theory (read at your own risk) - Stephan Snegirov
- vector bundles (read at your own risk) - Stephan Snegirov
- curves - Adam Holeman
- Tsen's theorem - Adam Holeman
- forms part 1 (read at your own risk) - Stephan Snegirov
- forms part 2 (read at your own risk) - Stephan Snegirov
- curves part 2 - Carlos Cortez
- curves part 3 - Carlos Cortez
- six functors part 0 (read at your own risk) - Stephan Snegirov
- cohomology of number fields - Eivind Hjelle
- shapes - Viktor Burghardt
- the shape of the integers - Viktor Burghardt

**Exercises, Solutions. The solutions shall be thought of as proof inspirations.
**

**References:**

- Milne's lecture notes
- Etale Cohomology Seminar at UIUC (Daniel Carmody)
- notes from a class by J. de Jong
- notes from a class by Prof. Dr. Uwe Jannsen
- notes Davide Lombardo & Andrea Maffei
- Fundamental Algebraic Geometry: Grothendieck's FGA Explained

organized by: Viktor Burghardt and Eivind Hjelle