| Résume | The l-adic pro-algebraic fundamental group is the universal objectclassifying smooth l-adic sheaves. For smooth varieties in finite and mixedcharacteristics, the it is largely determined as a Galois representation bycohomology of semisimple local systems, and the same holds for big Malcevcompletions. There are also a pro-algebraic crystalline fundamental groupand a non-abelian \'etale-crystalline comparison theorem. |
