$p$-adic monodromy of the universal deformation of a HW-cyclic Barsotti–Tate group

Yichao Tian

Documenta mathematica, Tome 14 (2009), pp. 397-440

Résumé

Let k be an algebraically closed field of characteristic p>0, and G be a Barsotti–Tate over k. We denote by S the “algebraic” local moduli in characteristic p of G, by G the universal deformation of G over S, and by U⊂S the ordinary locus of G. The étale part of G over U gives rise to a monodromy representation ρG​ of the fundamental group of U on the Tate module of G. Motivated by a famous theorem of Igusa, we prove in this article that ρG​ is surjective if G is connected and HW-cyclic. This latter condition is equivalent to saying that Oort's a-number of G equals 1, and it is satisfied by all connected one-dimensional Barsotti–Tate groups over k.

Détail

DOI : 10.4171/dm/277

Classification : 13D10, 14B12, 14D15, 14H30, 14L05, 14L15
Mots-clés : Barsotti-Tate groups (p-divisible groups), p-adic monodromy representation, universal deformation, Hasse-Witt maps