Deformation of a HW-Cyclic Barsotti-Tate Group

Let k be an algebrai ally losed eld of hara teristi p > 0, andG be a Barsotti-Tate over k. We denote by S the algebrai lo al moduli in hara teristi p of G, by G the universal deformation of G over S, and by U ⊂ S the ordinary lo us 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 arti le that ρG is surje tive if G is onne ted and HWy li . This latter ondition is equivalent to saying that Oort's a-number of G equals 1, and it is satis ed by all onne ted one-dimensional Barsotti-Tate groups over k. 2000 Mathemati s Subje t Classi ation: 13D10, 14L05, 14H30, 14B12, 14D15, 14L15