Le $S$ be a base scheme, $G$ be a fnite $S$-group scheme that acts on a $S$-group scheme $X$ such that the quotient exists. I know that the dimension of $X/G$ has to be the dimension of $X$ because $G$ is finite but I don't succeed in proving it. When does the dimension of the quotient "behave well" (namely when do we have $\dim(X/G) = \dim(X)-\dim(G)$)?
Many thanks for your answers!