Lecture on Algebraic Geometry III (H. Esnault/M. Kerz)

Topics: curves, coherent sheaves, invertible sheaves, divisors, sheaf cohomology, Riemann-Roch theorem, zeta function of curves over finite fields, Riemann hypothesis for curves.

Lecture: Monday 10-12 (T 03 R 04 D 10), Wednesday 10-12 (T 03 R 03 D 75)

Exercise session: Monday 18-20 (T 03 R 04 D 10)

Problem sets:

No. pdf due
1 link 11.4.
2 link 18.4.
3 link 26.4.
4 link 9.5.
5 link 16.5.
6 link 23.5.
7 link 30.5.
8 link 6.6.
9 link 13.6.
10 link 20.6.
11 link 27.6.
12 link 4.7.

Literature:

  • R. Hartshorne: Algebraic Geometry. Graduate Texts in Mathematics. Springer-Verlag, New York 1977.
  • S. Raskin (after A. Beilinson’s course): The Weil conjectures for curves. pdf
  • B. Poonen: Rational points on varieties. pdf