Galois characters associated to formal -modules
Galois extensions of height-one commuting dynamical systems
We consider a dynamical system consisting of a pair of commuting power series under composition, one noninvertible and another nontorsion invertible, of height one with coefficients in the -adic integers. Assuming that each point of the dynamical system generates a Galois extension over the base field, we show that these extensions are in fact abelian, and, using results from the theory of the field of norms, we also show that the dynamical system must include a torsion series. From an earlier...
Galois Properties of Torsion Points on Abelian Varieties.
Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of -kernel.
Geometry of an étale covering of the -adic upper half plane
We describe the rigid geometry of the first layer in the tower of coverings of the -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.
Group Schemes over artinian rings and Applications
Let be a positive integer and a complete characteristic zero discrete valuation ring with maximal ideal , absolute ramification index and perfect residue field of characteristic . In this paper we classify smooth finite dimensional formal -faithful groups over , i.e. groups on which the “multiplication by ” morphism is faithfully flat, in particular -divisible groups. As applications, we prove that -divisible groups over , and the morphisms between them, lift canonically to , and...
Groupes affines, commutatifs, unipotents sur un corps non parfait
Groupes de Lubin-Tate généralisés.
Groupes henséliens
Groupes -divisibles et modules filtrés : le cas peu ramifié
Groupes p-divisibles et corps gauches