  Those are the notes for the 2015 Summer Research Institute on Algebraic
Geometry. We report on Deligne's finiteness theorem for $\ell$-adic
representations on smooth varieties defined over a finite field, on its
crystalline version, and on how the geometric \'etale fundamental group of a
smooth projective variety defined over a characteristic $p>0$ field controls
crystals on the infinitesimal site and should control those on the crystalline
site. v2: last results added to the report, and some typos corrected.
