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.



Sketch of Weil's proof of the Riemann hypothesis for curves
There is an REU paper from Chicago which seems to cover it <https://math.uchicago.edu/~may/VIGRE/VIGRE2007/REUPapers/FINALFULL/Raskin.pdf>


