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arXiv · 2102.08999

Local Monodromy of 1-Dimensional p-Divisible Groups

Tristan Phillips
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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 $\rho$. The image of $\rho$ 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 \'etale part of $G$ is irreducible, generalizing a result of Chai.

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Tristan Phillips. 2021-02-17. Local Monodromy of 1-Dimensional p-Divisible Groups. https://doi.org/10.1016/j.jnt.2025.11.008

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