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

Source 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.