My naïve cartoon picture of the construction of étale cohomology is this:
- start with a scheme, associate to it a Grothendieck topology (making a site).
- A functor from the Grothendieck topology to abelian groups (say) has all the relevant properties of a presheaf (by the definition of a Grothendieck topology) and so one gets cohomology by sheafifying and taking (as it were) sheaf cohomology.
My question is: is there a “minimal” reference describing the second step above without caring about schemes or étale cohomology (the first step)? Of course, I don't mind if the reference covers étale cohomology, as long as steps 1 and 2 are separated.
Having formulated this question and anticipating the answer let me ask a second question: are there, among the first six exposés of SGA4, parts that I can skip while trying to learn about step 2?