Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" and by Liu - "Algebraic Geometry and Arithmetic Curves".
What would be a good learning path towards the proof of the Weil Conjectures for algebraic varieties (not just curves)?
What modern references are available and in which order should be studied?
Besides the original article I and article II by Deligne and the results on rationality by Dwork, there is the book Freitag/Kiehl - "Étale Cohomology and the Weil Conjecture" and the online pdf by Milne - "Lectures on Étale Cohomology". The first title is out of stock and hard to get and the second seems to me too brief and succinct.
- Is it better to master étale cohomology by itself elsewhere and then refer to the original articles? Is any further algebraic/arithmetic background necessary?
Thank you in advance for any hints on how to approach such a study program, and for any related advice towards a self-learning path in arithmetic geometry. (This question is cross posted to math.stackexchange so all kind of students and professionals can provide their advice regardless of their membership to these forums.)