Non-liftability of the field of norms of the $p$-adic false Tate curve extension

Let $p\geq3$ be a prime number. We prove that the action of the Galois group on the field of norms of the $p$-adic false Tate curve extension $\mathbf{Q}_p\left(ζ_{p^\infty},p^{1/p^\infty}\right)$ of $\mathbf{Q}_p$ is not liftable to its Cohen ring with respect to any admissible coefficient field.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.35006
Primary Topic
Advanced Algebra and Geometry
Type
preprint
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preprint

Non-liftability of the field of norms of the $p$-adic false Tate curve extension

Yijun Yuan
arXiv (Cornell University)
Advanced Algebra and Geometry
preprint

Non-liftability of the field of norms of the $p$-adic false Tate curve extension

Yijun Yuan
preprint en

Abstract

Let $p\geq3$ be a prime number. We prove that the action of the Galois group on the field of norms of the $p$-adic false Tate curve extension $\mathbf{Q}_p\left(ζ_{p^\infty},p^{1/p^\infty}\right)$ of $\mathbf{Q}_p$ is not liftable to its Cohen ring with respect to any admissible coefficient field.

arXiv (Cornell University)
Advanced Algebra and Geometry
DOIOpen Access PDFOpenAlex
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Non-liftability of the field of norms of the $p$-adic false Tate curve extension — Yijun Yuan · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS