Families of p-Divisible Groups with Constant Newton Polygon

ar X iv : m at h / 02 09 26 4 v 1 [ m at h . A G ] 2 0 Se p 20 02 1 Families of p - divisible groups with constant Newton polygon

Let X be a p-divisible group with constant Newton polygon over a normal noetherian scheme S. We prove that there exists an isogeny to X → Y such that Y admits a slope filtration. In case S is regular this was proved by N.Katz for dim S = 1 and by T.Zink for dim S ≥ 1.

Foliations in moduli spaces of abelian varieties

In this paper we study abelian varieties and of p-divisible groups in characteristic p. Even though a non-trivial deformation of an abelian variety can produce a non-trivial Galois-representation, say on the Tate-l-group of the generic fiber (in any characteristic), the geometric generic fiber has a “constant” Tate-l-group. The same phenomenon we encounter for the p-structure in positive charac...

On the Slope Filtration

Let X be a p-divisible group over a regular scheme S such that the Newton polygon in each geometric point of S is the same. Then there is a p-divisible group isogenous to X which has a slope filtration.

Strati cations and foliations of moduli spaces

We study the moduli spaces A = A g;1 F p of principally polarized abelian varieties in characteristic p, and also A g F p. The p-structure on the abelian varieties in consideration provides us with several naturally deened subsets. In this talk we discuss the deenitions and constructions of these sets, we indicate interrelations, and we sketch proofs, applications, open problems and conjectures...

Newton Polygons and P-divisible Groups: a Conjecture by Grothendieck