Local Monodromy of 1-Dimensional p-Divisible Groups
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912844461637632 |
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| author | Phillips, Tristan |
| author_facet | Phillips, Tristan |
| contents | 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 $ρ$. The image of $ρ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08999 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Local Monodromy of 1-Dimensional p-Divisible Groups Phillips, Tristan Number Theory 11S31 (primary), 14L05, 11S15 (secondary) 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 $ρ$. The image of $ρ$ 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. |
| title | Local Monodromy of 1-Dimensional p-Divisible Groups |
| topic | Number Theory 11S31 (primary), 14L05, 11S15 (secondary) |
| url | https://arxiv.org/abs/2102.08999 |