#### Title

Local Monodromy of p-Divisible Groups

#### Publication Date

2010

#### Journal or Book Title

Transactions of the American Mathematical Society

#### Abstract

A p-divisible group over a field K admits a slope decomposition; associated to each slope λ is an integer m and a representation Gal(K) → GLm(Dλ), where Dλ is the Qp-division algebra with Brauer invariant [λ]. We call m the multiplicity of λ in the p-divisible group. Let G0 be a p-divisible group over a field k. Suppose that λ is not a slope of G0, but that there exists a deformation of G in which λ appears with multiplicity one. Assume that λ 6= (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(Dλ) has large image.

#### Volume

362

#### Pages

985-1007

#### Issue

2

#### Recommended Citation

Achter, JD and Norman, P, "Local Monodromy of p-Divisible Groups" (2010). *Transactions of the American Mathematical Society*. 747.

Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/747