  Let $(G,X)$ be a Shimura pair of Hodge type such that $G$ is the
Mumford--Tate group of some elements of $X$. We assume that for each simple
factor $G_0$ of $G^{\ad}$ there exists a simple factor of $G_{0\dbR}$ which is
compact. Let $N\Ge 3$. We show that for many compact open subgroups $K$ of
$G(\dbA_f)$, the Shimura variety $\Sh(G,X)/K$ has a projective integral model
$\scrN$ over $\dbZ[{1\over N}]$ which is a finite scheme over a certain Mumford
moduli scheme $\scrA_{g,1,N}$. Equivalently, we show that if $A$ is an abelian
variety over a number field and if the Mumford--Tate group of $A_{\dbC}$ is
$G$, then $A$ has potentially good reduction everywhere. The last result
represents significant progress towards the proof of a conjecture of Morita. If
$\scrN$ is smooth over $\dbZ[{1\over N}]$, then it is a N\'eron model of its
generic fibre. In this way one gets in arbitrary mixed characteristic, the very
first examples of general nature of projective N\'eron models whose generic
fibres are not finite schemes over abelian varieties.
