Abstract :
Mumford (Math. Ann. 181 (1969) 345–351) constructs families of abelian varieties which are parametrized by Shimura varieties but which are not of PEL type. In this paper we investigate Mumfordʹs families. We notably determine, for each fibre of such a family over a number field, the possible isogeny types and the possible Newton polygons of its reductions. In the process, a classification of the CM points on Mumfordʹs Shimura varieties is obtained.
