Séminaire de Théorie des Nombres de Montpellier :

Le 03 avril 2006 à 15:00 - salle 431

Présentée par Zink Thomas - Universität Bielefeld

« The slope-filtration for p-divisible groups and purity of the Newton polygon »

The p-adic valuation of the Frobenius endomorhism acting on the cohomology can be described by the Newton polygon. We discuss the behaviour of the Newton polygon in agebraic families. If the Newton polygon in a family of p-divisible groups is constant, then the family becomes constant up to isogeny after extension of the base. This was first found by Katz and later generalized by Oort and Zink. As an application we give a new approach to the purity theorem of Oort and de Jong.