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Assume I have a surjective morphism of algebraic group schemes over $\mathbb{Q}_p$, $\mathcal{G}\longrightarrow S$, equipped with a section, and assume both of these group schemes are equipped with an ...

Let $\mathbf{G}$ be a split connected reductive group scheme over a scheme $X$. Let $X'\rightarrow X$ an étale Galois cover of group $\Gamma$. We consider $G$ a quasi-split group scheme over $X$ ...