Schottky uniformization theory on Riemann surfaces and Mumford curves of infinite genus.
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...
On étudie le comportement des faisceaux -adiques entiers sur les schémas de type fini sur un corps local par les six opérations et le foncteur des cycles proches.
On étudie les espaces de Stein quasi-compacts (i.e. vérifiant pour tout et tout faisceau cohérent sur ). On établit un critère simple pour qu’un espace soit de Stein et on en déduit quelques conséquences.