Revêtements de la droite affine en caractéristique p>0 et conjecture d'Abhyankar.
We study local properties of quasi-unipotent overconvergent -isocrystals on a curve over a perfect field of positive characteristic . For a --module over the Robba ring , we define the slope filtration for Frobenius structures. We prove that an overconvergent -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.
We recall some basic constructions from -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of -pairs, introduced recently by Berger, which provides a natural enlargement of the category of -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...