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

Yijun Yuan

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arXiv · 2610.35006

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

Yijun Yuan

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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.

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Yijun Yuan. 2026-10-26. Non-liftability of the field of norms of the $p$-adic false Tate curve extension. https://arxiv.org/abs/2610.35006

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