Geodesic
Stratifications of Newton polygon strata and Traverso’s conjectures for $p$-divisible groups
Eike Lau1 ; Marc-Hubert Nicole2 ; Adrian Vasiu3
1 Universität Paderborn, Paderborn, Germany
2 Institut mathématique de Luminy, Marseille, France
3 Binghamton University, Binghamton, NY
Annals of mathematics, Tome 178 (2013) no. 3, pp. 789-834.

Voir la notice de l'article provenant de la source Annals of Mathematics website

The isomorphism number (resp. isogeny cutoff) of a $p$-divisible group $D$ over an algebraically closed field of characteristic $p$ is the least positive integer $m$ such that $D[p^m]$ determines $D$ up to isomorphism (resp. up to isogeny). We show that these invariants are lower semicontinuous in families of $p$-divisible groups of constant Newton polygon. Thus they allow refinements of Newton polygon strata. In each isogeny class of $p$-divisible groups, we determine the maximal value of isogeny cutoffs and give an upper bound for isomorphism numbers, which is shown to be optimal in the isoclinic case. In particular, the latter disproves a conjecture of Traverso. As an application, we answer a question of Zink on the liftability of an endomorphism of $D[p^m]$ to $D$.
DOI : 10.4007/annals.2013.178.3.1

Eike Lau 1 ; Marc-Hubert Nicole 2 ; Adrian Vasiu 3

1 Universität Paderborn, Paderborn, Germany
2 Institut mathématique de Luminy, Marseille, France
3 Binghamton University, Binghamton, NY 
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Eike Lau; Marc-Hubert Nicole; Adrian Vasiu. Stratifications of Newton polygon strata and Traverso’s conjectures for $p$-divisible groups. Annals of mathematics, Tome 178 (2013) no. 3, pp. 789-834. doi : 10.4007/annals.2013.178.3.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.1/

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