  We give several generalisations of the Deuring reduction criterion for
elliptic curves to abelian varieties of higher dimension. In particular the
Newton polygon of the reduction of an abelian variety A with complex
multiplication by F at a prime above p can be explicitly computed in terms of
the CM type of A and the decomposition group of a suitable prime above p in a
Galois closure of F. Conversely, it is shown that the formal isogeny type of
the reduction of A at a prime above p places certain restrictions on the
decomposition of p in F.
