See the syllabus. For the Summer of 2022, we will be discussing the basics of etale cohomology with the goal of understanding Deligne's proof of the Weil conjectures under the supervision of Romyar Sharifi. We are primarily following the treatment of Freitag and Kiehl, supplemented with notes from J.S. Milne and Brian Conrad, as well as references to the Stacks Project.
| Date | Topic | Speaker | Notes |
|---|---|---|---|
| 6/15/22 | Introduction | Jas Singh | weil-intro.pdf |
| 6/21/22 | Etale morphisms and their properties | Jacob Swenberg | |
| 6/28/22 | Etale morphisms, formally | Jacob Swenberg | |
| 7/1/22 | Etale fundamental groups | Jas Singh | weil-etale-fundamental-groups.pdf |
| 7/5/22 | Sites | Colin Ni | |
| 7/8/22 | Etale sheaves | Jacob Swenberg | |
| 7/12/22 | Etale cohomology of curves | Jas Singh | weil-cohomology-of-curves.pdf |
| 7/15/22 | Constructible sheaves | Rohan Joshi | |
| 7/19/22 | Proper base change | Jacob Swenberg | |
| 7/22/22 | Smooth base change I | Rohan Joshi | |
| 7/26/22 | Smooth base change II | Colin Ni | |
| 7/29/22 | l-adic sheaves | Jacob Swenberg | |
| 8/2/22 | Poincare/Verdier duality I | Rush Brown | |
| 8/5/22 | Poincare/Verdier duality II | Rush Brown | |
| 8/9/22 | Comparison theorems | Jas Singh | weil-etale-analytic-comparison.pdf |
| 8/12/22 | Frobenius and the Grothendieck--Lefschetz trace formula | Rohan Joshi | |
| 8/16/22 | Lefschetz pencils | Colin Ni | |
| 8/19/22 | Monodromy of Lefschetz pencils I | Jacob Swenberg | |
| 8/23/22 | Monodromy of Lefschetz pencils II | Jacob Swenberg | |
| 8/26/22 | Global Monodromy of Lefschetz pencils | Jas Singh | weil-global-monodromy.pdf |
| 8/30/22 | Proving the Weil Conjectures I | Jacob Swenberg | |
| 9/2/22 | Proving the Weil Conjectures II | Jas Singh | weil-proofs-and-rh-reductions.pdf |
| 9/6/22 | Deligne's proof III | Jacob Swenberg | |
| 9/9/22 | Applications/Generalizations | Jas Singh | weil-coda.pdf |