Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-Tate
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917530716602368 |
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| author | Kondo, Kaiji |
| author_facet | Kondo, Kaiji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-Tate Kondo, Kaiji Number Theory 11S20, 11S31, 11F80 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. |
| title | Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-Tate |
| topic | Number Theory 11S20, 11S31, 11F80 |
| url | https://arxiv.org/abs/2605.25428 |