08/14 Lecture 1. The Frobenius morphism.
08/16 Lecture 2. Properties of Frobenius.
08/21 Lecture 3. Curves over finite fields: first examples.
08/23 Lecture 4. Points on the Fermat curve.
08/28 Lecture 5. The Riemann hypothesis I: intersection theory on surfaces.
08/30 Lecture 6. The Riemann hypothesis II: proof.
09/04 Lecture 7. The Zeta function of the Fermat curve.
09/06-13 Lectures 8 and 9. Proof of the Weil conjectures for curves.
09/20-25 Lectures 10 and 11. Zeta functions of elliptic curves.
09/27 Lecture 12. Rational and unirational surfaces. (Shioda's paper)
10/02 Lecture 13. The Noether-Enriques criterion.
10/04 Lecture 14. The Castelnuovo criterion (overview).
10/09 Lecture 15. Picard ranks. (sage code, Schütt-Shioda-van Luijk's paper)
10/11 Lecture 16. Bounds on Picard rank.
10/16 Lecture 17. Serre's example.
10/23 Lecture 19. Witt vectors I. (Rabinoff's notes)
10/25 Lecture 20. Witt vectors II.
10/30 Lecture 21. Witt vectors III.
11/01-06 Lecture 22. Deformation theory of smooth varieties.
11/08-15 Lecture 23. Formal lifts and algebraization.
11/27 Lecture 24. Lifting abelian varieties.