Let $k$ be a finite field, and $A$, $B$ abelian varieties over $k$. Let $T\_p(A)$, $T\_p(B)$ be
the (contravariant) Dieudonn\'e modules associated to the p-divisible groups attached to $A$ and $B$, respectively. The theorem of Tate in the question is that the natural map


${\rm Hom}\_k(A,B)\otimes\mathbf{Z}\_p\longrightarrow{\rm Hom}(T\_p(B),T\_p(A))$


is an isomorphism.


It seems to me that the standard reference for the proof of this theorem is a paper of Tate titled *Endomorphisms of abelian varieties over finite fields. II* that should have appeared 50 years ago in Inventiones but, I am right, never did.


Is there another reference in the literature for the proof of this theorem?


Thanks.



Reference for a theorem of Tate on the endomorphism rings of AVs over finite fields
I think the result appears in:


Waterhouse, W. C.; Milne, J. S.: Abelian varieties over finite fields. 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969), pp. 53–64. Amer. Math. Soc., Providence, R.I., 1971


