Families of p-divisible groups with constant Newton polygon

A p-divisible group over a base scheme in characteristic p in general does not admit a slope filtration. Let X be a p-divisible group with constant Newton polygon over a normal noetherian scheme S; we prove that there exists an isogeny from X to 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) > 0. We give an example of a p-divisible group over a non-normal base which does not admit an isogeny to a p-divisible group with a slope filtration.Comment: To be published in Documenta Mathematic

Moduli of abelian varieties and p-divisible groups

Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.Comment: 92 page

Velocity control of a 2D dynamic walking robot

In this abstract we introduce velocity control for our 2D dynamic walking robot Dribbel [1] (figure 1) and show that, by ‘closing the loop’, this automatically leads to increased robustness

Geometric dynamics analysis of humanoids - locked inertia

The advantage of geometric dynamics analysis over most classical 3D analysis is that the equations are coordinate- neutral: as long as all quantities are expressed in the same coordinate frame, the equations are correct