TITLE: Sketch of Weil's proof of the Riemann hypothesis for curves
QUESTION [6 upvotes]: I was wondering if anybody could provide a sketch of Weil's proof of the Riemann hypothesis for curves that uses the Jacobian $\text{Pic}^0(X)$ and a bit of the intersection theory on $X \times X$ and the underlying intuitions.
The previous version of this question was asking for  a "proof without words", which I realize now was a silly thing to ask for.

REPLY [5 votes]: Alexander Beilinson gave four lectures on this topic (probably, during the same REU). Unfortunately, right now the link is not working, but maybe someone could provide another link?
Also, in Manin’s “Cubic Forms: Algebra, Geometry, Arithmetic” one can find beautiful and self-contained exposition of the Weil conjectures for del Pezzo surfaces (and some arithmetic applications).