Towards Non-Abelian p-adic Hodge Theory in the Good Reduction Case

We develop a non-abelian version of p-adic Hodge Theory for varieties (possibly open with "nice compactification") with good reduction. This theory yields in particular a comparison between smooth p-adic sheaves and F-isocrystals on the level of certain Tannakian categories, p-adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups. © 2010 American Mathematical Society.