Prof. Dr. Timo Richarz

**Contact**

M.Sc. Patrick Bieker

Email: bieker (ergänze @mathematik.tu-darmstadt.de)

**Time and Place**

Wednesdays, 09:50-11:30 in S1|02-144

Starting: 17.04.2019

**Contents**

The course is an introduction to the Weil Conjectures. We start with Congruences and Zeta functions, formulate the Weil Conjectures, make the connection to étale cohomology and discuss elements of the proof starting with the case of curves.

Prerequisites are basic algebraic geometry such as Hartshorne, §§2-3 and étale cohomology, e.g., as covered in the last winter term. Constructions in étale cohomology relevant to the course will be stated during the lecture with details to be discussed in a block seminar, see exercise session below.

**Literature**

- A. Weil: Numbers of Solutions of Equations in finite fields.
- P. Deligne: La conjecture de Weil I & II, Publ. math. de l’I.H.É.S.
- N. Katz: An overview of Deligne’s proof of the Riemann hypothesis for varieties over finite fields.
- E. Freitag, R. Kiehl: Etale Cohomology and the Weil Conjecture, Springer.

**Exercise session**

M.Sc. Patrick Bieker

This will be in form of a block seminar accompanying the lectures. We cover topics in étale cohomology such as the Lefschetz trace formula which are used, but not proven throughout the lectures and complement the topics from last semester. Here is the plan.

**Exam**

This is an oral exam. For further information contact the lecturer.