Teaching
This semester I am teaching Étale cohomology 2.
Time/Place:
- Lectures: Tuesdays and Thursdays 11:00-13:00, Mathematikon, SR 3.
- Exercises (Christian Dahlhausen): Thursdays 16:00 - 18:00, Mathematikon SR4.
- Exam: oral
Program:
The goal will be to give a full proof of the Weil conjectures. The program will focus on:
- Smooth base change and applications
- Duality
- Trace formulas and proof of the conjectures (except Riemann hypothesis)
- Lefschetz's pencils and proof of the Riemann hypothesis
As a technical tool, constructions will be presented in the context of derived DG categories. This is a compromise between the classical triangulated picture (whose problems will be evidenced) and the modern ∞-categorical perspective (which would require too much background).
The script and exercise sheets will be published on MaMpf
Bibliography:
- Our primary guideline will be:
- Deligne, Étale cohomology, SGA4 1/2 (in French, available online, scanned and typed)
- Another reference is
- Freitag--Kiehl, Étale cohomology and the Weil conjectures (available online)
- The reference for the Riemann hypothesis is
- Deligne, La Conjecture de Weil I (available online and also translated by Goncharov and Milne)
- Some parts have been simplified, so we will sometimes refer to lemmas and theorems in:
- The Stacks Project chapters 59 and 63