Abstract:  I will talk about Katz' method of proving the Riemann hypothesis (RH) for hypersurfaces. The basic idea is very similar to what we saw last time: We reduce to showing RH for a particular hypersurface. Then we show RH for this particular hypersurface by a point-counting argument.

Reference: Katz, A note on Riemann hypothesis for curves and hypersurfaces over finite fields, Sections 5-8.