PreprintarXiv licencearXiv
The order types of the supports of p-adic algebraic Hahn series
Abstract
Let p be a prime number. In 1986, David Lampert asked if one expands a Qp-algebraic number as a p-adic Hahn series, then what is the possible order type of its support? In 2001, Kedlaya made a vague conjecture that the possible ordinals can only be finite ordinals, ω and ωω, where ω is the first infinite ordinal. In this article, we solve Lampert's problem by confirming Kedlaya's intuition. Moreover, we completely characterize the Qp-algebraic numbers with order type of support at most ω. As an application, we determine the bi-algebraic set of the p-adic shadow map.
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BibTeX
@misc{wang2026order,
title = {{The order types of the supports of $p$-adic algebraic Hahn series}},
author = {Shanwen Wang and Yijun Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13014},
eprint = {2610.13014},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13014},
}
RIS
TY - UNPB
TI - The order types of the supports of p-adic algebraic Hahn series
AU - Shanwen Wang
AU - Yijun Yuan
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13014
UR - https://arxiv.org/abs/2610.13014
AB - Let p be a prime number. In 1986, David Lampert asked if one expands a Q_p-algebraic number as a p-adic Hahn series, then what is the possible order type of its support? In 2001, Kedlaya made a vague conjecture that the possible ordinals can only be finite ordinals, ω and ω^ω, where ω is the first infinite ordinal. In this article, we solve Lampert's problem by confirming Kedlaya's intuition. Moreover, we completely characterize the Q_p-algebraic numbers with order type of support at most ω. As an application, we determine the bi-algebraic set of the p-adic shadow map.
ER -