Math 732. Zeta functions in algebraic geometry
Lecture 1. Zeta functions: an overview
Lecture 2. The Hasse-Weil zeta function: definition and elementary properties
Lecture 3. The statements of the Weil conjectures
Lecture 4. The Weil conjectures for curves
Lecture 5. Weil cohomology theories and the Weil
conjectures
Lecture 6. Fulton's trace formula for coherent sheaf cohomology
Lecture 7. The Lang-Weil estimate and the zeta function of an arithmetic
scheme
Lecture 8. The Grothendieck ring of varieties and Kapranov's motivic zeta function
Lecture 9. Dworks's proof of the rationality of the
Hasse-Weil zeta function
Appendix 1. Quotients by finite group actions, and
ground field extensions of algebraic varieties
Appendix 2. Basics of p-adic fields