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

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).