  Assume that $X$ and $Y$ are arithmetic schemes, i.e., integral schemes of
finite types over $Spec(\mathbb{Z})$. Then $X$ is said to be quasi-galois
closed over $Y$ if $X$ has a unique conjugate over $Y$ in some certain
algebraically closed field, where the conjugate of $X$ over $Y$ is defined in
an evident manner. Now suppose that $\phi:X\to Y$ is a surjective morphism of
finite type such that $X$ is quasi-galois closed over $Y$. In this paper the
main theorem says that the function field $ k(X)$ is canonically a Galois
extension of $k(Y)$ and the automorphism group ${Aut}(X/Y)$ is isomorphic to
the Galois group $Gal(k(X)/k(Y))$; in particular, $\phi$ must be affine.
Moreover, let $\dim X=\dim Y$. Then $X$ is a pseudo-galois cover of $Y$ in the
sense of Suslin-Voevodsky.
