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 14:00 - 16:00, 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