I am interested in etale cohomology of varieties, and respectively, in mixed $\mathbb Q_{\ell}$-adic Galois representations over finitely generated fields. What is the canonical reference for this definition and its relation to etale cohomology? I cannot find an explicit definition (in the case where the base field is neither finite nor $\mathbb Q$) in Deligne's Weil II. Note also that Jannsen's "Weights in arithmetic geometry" neither contains the proofs nor precise references to them.
Respectively, may I ask you to give a precise reference (if you will cite something long and French)?
