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Slope filtration of quasi-unipotent overconvergent F -isocrystals

Nobuo Tsuzuki (1998)

Annales de l'institut Fourier

We study local properties of quasi-unipotent overconvergent F -isocrystals on a curve over a perfect field of positive characteristic p . For a φ - -module over the Robba ring , we define the slope filtration for Frobenius structures. We prove that an overconvergent F -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.

Some new directions in p -adic Hodge theory

Kiran S. Kedlaya (2009)

Journal de Théorie des Nombres de Bordeaux

We recall some basic constructions from p -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B -pairs, introduced recently by Berger, which provides a natural enlargement of the category of p -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...

Sur les espaces de Stein quasi-compacts en géométrie rigide

Qing Liu (1989)

Journal de théorie des nombres de Bordeaux

On étudie les espaces de Stein quasi-compacts X (i.e. vérifiant H q ( X , ) = 0 pour tout q 1 et tout faisceau cohérent sur X ). On établit un critère simple pour qu’un espace soit de Stein et on en déduit quelques conséquences.

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