Speaker: Jane Shi (MIT)

Title: Katz's proof of the Riemann hypothesis for curves

Abstract:

In this talk, we'll study a proof of the Riemann Hypothesis for (projective, smooth and  geometrically connected) curves over finite fields by Katz. We'll study Deligne's version of Rankin's method and the "connect by curves" lemma, and how they reduce a proof of RH on genus $g$ curves to a proof of RH on Fermat curves. Finally, we'll introduce the "persistence of purity theorem", which will be useful for the next talk.

Reference:  section 1-4 of A Note on Riemann Hypothesis for Curves and Hypersurfaces Over Finite Fields.