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Lubin-Tate representations over nontrivial finite Galois extensions of ℚp are not Aut-intrinsically Hodge-Tate
Abstract
In the present paper, we show that, for an odd prime number p and a nontrivial finite Galois extension k of ℚp, 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 ℚp 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.
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BibTeX
@misc{kondo2026lubintate,
title = {{Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbbQ_p$ are not Aut-intrinsically Hodge-Tate}},
author = {Kaiji Kondo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.25428},
eprint = {2605.25428},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25428},
}
RIS
TY - UNPB
TI - Lubin-Tate representations over nontrivial finite Galois extensions of ℚ_p are not Aut-intrinsically Hodge-Tate
AU - Kaiji Kondo
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2605.25428
UR - https://arxiv.org/abs/2605.25428
AB - In the present paper, we show that, for an odd prime number p and a nontrivial finite Galois extension k of 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 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.
ER -