I'm currently interested in the cardinality of the set of values of a polynomial over a finite field.

I found a paper

Saburo Uchiyama,

Sur le Nombre des Valeurs Distinctes d'un Polynome a Coefficients dans un Corps Fini, Proceedings of the Japan Academy30, Issue 10 (1954) p. 930–933, doi:10.3792/pja/1195525873, Project Euclid.

In the paper, the author uses some theorem of Weil on an asymptotic formula of the cardinality of the zero set of an absolutely irreducible polynomial $f^{\ast}(u,v)=\frac{f(u)-f(v)}{u-v}$.

So I want to study 'quickly' Weil's theorem on this occasion. But the 1948 book of Weil 'Sur les courbes algébriques et les variétés qui s'en déduisent' (WorldCat) seems to be out of print and might not be modern.

I have a little familiarity with the first 3 chapters of Hartshorne.

I hope someone can recommend a reference. Thank you.