 
Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Pages 000000
S 00029947(XX)00000
LOCAL MONODROMY OF pDIVISIBLE GROUPS
JEFFREY D. ACHTER AND PETER NORMAN
Abstract. A pdivisible group over a field K admits a slope decomposition;
associated to each slope is an integer m and a representation Gal(K)
GLm(D), where D is the Qpdivision algebra with Brauer invariant [].
We call m the multiplicity of in the pdivisible group. Let G0 be a p
divisible group over a field k. Suppose that is not a slope of G0, but that
there exists a deformation of G in which appears with multiplicity one.
Assume that = (s  1)/s for any natural number s > 1. We show that there
exists a deformation G/R of G0/k such that the representation Gal(Frac R)
GL1(D) has large image.
1. Introduction
Given a rational number [0, 1], where = r/s with gcd(r, s) = 1, let
H be the pdivisible group defined over Fp whose covariant DieudonnŽe module
is generated by a single generator e satisfying the relation (Fsr
 V r
