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$\newcommand{\Lie}{\operatorname{Lie}}$Let $G$ be a smooth linear algebraic variety over perfect field $k$, acting on a separated variety $X$, and for $x \in X(k)$ write $G_x$ for the scheme-theoretic ...

I am interested in orbits of the action of a group scheme on a scheme and I'm particularly interested in the following special case: Let $k$ be an algebraically closed field, let $G$ be an affine ...