I know that the Weil's proof of the *Weil conjectures for curves and abelian varieties* is made under the lenguage of his "Foundation of algebraic geometry", however in "Polarizations and Grothendieck's Standard conjectures" Milne says:

In examining Weil’s proofs (Weil 1948) of the Riemann hypothesis for curves and abelian varieties over finite fields, Grothendieck was led to state two “standard” conjectures (Grothendieck 1969), which imply the Riemann hypothesis for all smooth projective varieties over a finite field, essentially by Weil’s original argument.

Is there a proof of the *Weil conjectures for curves and abelian varieties* in modern (mathematical)language such that follows the Weil's original argument?