Let $(\{X_{0},X_{1}\},\{d_{0},d_{1} : X_{1} \to X_{0}\})$ be a groupoid in schemes. In SGA 3, Exp. V, section 5 a), the following is claimed, where I think it is being assumed that $d_{0}$ and $d_{1}$ are finite flat:
Let $U^{(n)}$ be the largest open subset of $X_{0}$ over which $d_{1}$ is finite locally free of rank $n$. We know that $X_{0}$ is the disjoint union of the $U^{(n)}$.
Is this true even if $X_{0}$ is not locally Noetherian? Am I missing something?