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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.

Specializations of one-parameter families of polynomials

Farshid Hajir, Siman Wong (2006)

Annales de l’institut Fourier

Let K be a number field, and suppose λ ( x , t ) K [ x , t ] is irreducible over K ( t ) . Using algebraic geometry and group theory, we describe conditions under which the K -exceptional set of λ , i.e. the set of α K for which the specialized polynomial λ ( x , α ) is K -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed n 10 , all but finitely many K -specializations of the degree n generalized Laguerre polynomial L n ( t ) ( x ) are K -irreducible and have Galois group S n . Second, we study specializations...

Sur le Topos infinitésimal p -adique d’un schéma lisse I

Alberto Arabia, Zoghman Mebkhout (2010)

Annales de l’institut Fourier

Afin de disposer des opérations cohomologiques aussi souples que possible pour la cohomologie de de Rham p -adique, le but principal de ce mémoire est de résoudre intrinsèquement du point de vue cohomologique le problème des relèvements des schémas lisses et de leurs morphismes de la caractéristique p > 0 à la caractéristique nulle ce qui a été l’une des difficultés centrales de la théorie de la cohomologie de de Rham des schémas algébriques en caractéristique positive depuis le début. Nous montrons...

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