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