Points counting and Serre's example. 2. Zeta functions and curves over finite fields. 3. Weil cohomology. 4. Kähler differentials 5. Étale morphisms. 6. Regularity. 7. Étale fundamental groups I. 8. Galois categories. 9. Henselian rings. 10. Étale fundamental groups II
In the summer semester of 2023, I supervised a reading group on Étale Cohomology and Weil Conjectures (as a supplement to Bruno Klingler's course). The covered topics were: 1. p-adic integration on Calabi-Yau varieties after Batyrev. 2. Betty numbers of moduli spaces of sheaves on surfaces after Yoshiyoka. 3. Weil Conjectures for K3 surfaces after Deligne. 5. Weil Conjectures for abelian varieties and curves after Ji. 6. Pro-étale sites after Bhatt&Scholze.