Gabber has a construction of the cat of l-adic sheaves, I think mentioned in a review of a Jannsen paper.
Ivorra is an expert on l-adic realization functors from various cats of mixed motives.
http://mathoverflow.net/questions/32478/a-nice-explanation-of-what-is-a-smooth-l-adic-sheaf
nLab page on l-adic sheaves