I'm currently trying to understand the construction of the category of l-adic constructible sheaves as in SGA5, and it seems that quite a lot of machinery (the MLAR condition, localization of the category of projective systems, etc.) has to be gone through before one can even construct this category and show that it's abelian, for instance. On the other hand it is not even true that the derived category of l-adic sheaves is defined in the obvious manner, since it is defined as a 2-limit of the derived categories of $\mathbb{Z}/l^n$ constructible sheaves.


I understand that the categorical machinery in existence today is a lot more powerful than it was in the 1970's, which makes me curious: is there a cleaner and more transparent way of doing this, and a more modern presentation than SGA or Frietag-Kiehl?



The category of l-adic sheaves
Section 1.4 in [these notes](http://math.unice.fr/~dehon/CohEtale-09/Elencj_Etale/CONRAD%2520Etale%2520Cohomology.pdf) of Brian Conrad is as nice as one could hope for, given the dryness of the adic formalism. I don't think the material differs substantially from Frietag-Kiehl, except in that the presentation is much cleaner. For the derived category stuff, the notes refer to Behrend's paper ["Derived $\ell$-adic Categories for Algebraic Stacks"](http://www.math.ubc.ca/~behrend/ladic.pdf) which I haven't looked at really, but a brief skim suggests it contains everything you might desire (constructions in *extremely* general situations), but nonetheless includes examples (!).


