The Weil Conjectures

TCC Course, Michaelmas 2017
Paul Ziegler

The Weil Conjectures, now a theorem, relate the problem of counting the number of points of varieties over finite fields to the geometry of such varieties. They can also be seen as an analogue of the Riemann Hypothesis over finite fields. I will introduce this result and give an overview over its proof.

Slides from the lectures: Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Exercises: Exercise Sheet
Credit: If you'd like to get credit for this class, please solve and turn in the exercise sheet.
Prerequisites: I will assume a basic knowledge of algebraic geometry and homological algebra as well as some experience with cohomology theories from algebraic topology.
References: √Čtale cohomology and the Weil conjecture, Eberhard Freitag and Reinhardt Kiehl.
√Čtale cohomology, James Milne.