Étale Homotopy Study Group

In Autumn 2020, I organised a study group designed for PhD students as an introduction to étale homotopy. The goal of the study group was to first define the étale homotopy type of a variety, and then define the étale homotopy obstruction to rational points on the variety. We mainly followed a paper of Harpaz and Schlank, though we also looked at parts of a paper by Ambrus Pál, and for the first few weeks, there are some excellent notes made by Schlank and Skorobogatov.

Details about the original schedule can be found in this pdf, though some talks diverged from this schedule slightly, and due to various scheduling reasons, the study group accelerated a bit towards the end. If have any questions or comments about the material here, please get in touch. 

1. (28/09) - Introduction to obstructions to rational points - Soham Karwa (LSGNT - Imperial)

2. (05/10) - Simplicial Homotopy I - Ashwin Iyengar (LSGNT - King's): Notes

3. (05/10) - Simplicial Homotopy II - Nick Sale (Swansea) : Notes

4. (12/10) - The Étale Homotopy Type - Jef Laga (Cambridge): Notes

5. (12/10) - The Relative Étale Homotopy Type - Jesse Pajwani (LSGNT - Imperial): Notes

6. (19/10) - Homotopy Fixed Points - Jesse Pajwani (LSGNT - Imperial): Notes

7. (19/10) - p-adic Homotopy Fixed Points and the Étale Homotopy Obstruction - Milton Lin (Taipei): Notes

8. (26/10) - Homotopy Fixed Point Theorems - Jesse Pajwani (LSGNT - Imperial): (Notes are the same as the next one)

9. (26/10) - The 2 truncation determines the étale homotopy obstruction - Jesse Pajwani (LSGNT - Imperial): Notes 

10. (02/11) - Connection to Finite Descent I & II - Jesse Pajwani (LSGNT - Imperial): Notes 

11. (17/11) - The Main Theorem - Jesse Pajwani (LSGNT - Imperial): Notes