# Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups - Mathematics > Algebraic Geometry

Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: The isomorphism number resp. isogeny cutoff of a p-divisible group D overan algebraically closed field is the least positive integer m such that Dp^mdetermines D up to isomorphism resp. up to isogeny. We show that theseinvariants are lower semicontinuous in families of p-divisible groups ofconstant Newton polygon. Thus they allow refinements of Newton polygon strata.In each isogeny class of p-divisible groups, we determine the maximal value ofisogeny cutoffs and give an upper bound for isomorphism numbers, which is shownto be optimal in the isoclinic case. In particular, the latter disproves aconjecture of Traverso. As an application, we answer a question of Zink on theliftability of an endomorphism of Dp^m to D.

Author: ** Eike Lau, Marc-Hubert Nicole, Adrian Vasiu**

Source: https://arxiv.org/