Weil conjectures 3: Riemann hypothesis

This talk is about the Stepanov-Bombieri proof of the Riemann hypothesis
for curves over a finite field. The proof works by finding a nonzero function that vanishes to high order at all points of the curve defined over the finite field Fq, and has a single pole of known order. The proof is elementary in the sense that it uses the Riemann-Roch theorem but no higher dimensional algebraic geometry.

For some details of the proof not in the lecture see Bombieri's paper