Local Monodromy of 1-Dimensional p-Divisible Groups

Abstract

Let $G$ be a $p$-divisible group over a complete discrete valuation ring $R$ of characteristic $p$. The generic fiber of $G$ determines a Galois representation $\ddot{I}$. The image of $\ddot{I}$ admits a ramification filtration and a Lie filtration. We relate these filtrations in the case $G$ is one dimensional, giving an equicharacteristic version of Sen's theorem in this setting. This result generalizes a result of Gross. Additionally, we prove that the representation associated to the étale part of $G$ is irreducible, generalizing a result of Chai.

21 pages. Many changes made in response to corrections and suggestions of referees