Let be an algebraically closed field of characteristic , and be a Barsotti–Tate over . We denote by the “algebraic” local moduli in characteristic of , by the universal deformation of over , and by the ordinary locus of . The étale part of over gives rise to a monodromy representation of the fundamental group of on the Tate module of . Motivated by a famous theorem of Igusa, we prove in this article that is surjective if is connected and HW-cyclic. This latter condition is equivalent to saying that Oort's -number of equals 1, and it is satisfied by all connected one-dimensional Barsotti–Tate groups over .
Cite this article
Yichao Tian, -adic monodromy of the universal deformation of a HW-cyclic Barsotti–Tate group. Doc. Math. 14 (2009), pp. 397–440DOI 10.4171/DM/277