Abstract:In the present paper, we show that, for an odd prime number $p$ and a nontrivial finite Galois extension $k$ of $\mathbb{Q}_{p}$, the $p$-adic representation of the absolute Galois group of $k$ determined by a Lubin-Tate formal group over the ring of integers of $k$ is not Aut-intrinsically Hodge-Tate [in the sense of Hoshi].
This settles the odd-degree cases left open in the previous works of Hoshi and the author and, together with the known even-degree case, completes the picture for finite Galois extensions of $\mathbb{Q}_{p}$ in the case where $p$ is odd.
This exhibits a sharp contrast, from the viewpoint of anabelian geometry, between the $p$-adic cyclotomic character and other $p$-adic Lubin-Tate characters.
| Subjects: | Number Theory (math.NT) |
| MSC classes: | 11S20, 11S31, 11F80 |
| Cite as: | arXiv:2605.25428 [math.NT] |
| (or arXiv:2605.25428v1 [math.NT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25428 arXiv-issued DOI via DataCite (pending registration) |
From: Kaiji Kondo [view email]
[v1]
Mon, 25 May 2026 05:09:10 UTC (10 KB)
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