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Let $K=\mathbb{Q}_p$ and $G$ a split reductive group over $K$ with split maximal torus $T$. Furthermore, $X$ is a smooth projective variety over $K$ with a free $G$-action. Let $U \subset X$ be a $T$-...

Here is a natural question that I hope will be of interest to some. Let $\mathbf{F}_p(\!(T)\!)$ be the field of formal Laurent series over $\mathbf{F}_p$. An automorphism of $\mathbf{F}_p(\!(T)\!)$ ...