### Group structures of elementary supersingular abelian varieties over finite fields, by Hui Zhu

Let A be a supersingular abelian variety over a finite field k. We
give an approximate description of the structure of the group A(k) of
rational points of A over k in terms of the characteristic polynomial
f of the Frobenius endomorphism of A relative to k. If f=g^e for a
monic irreducible polynomial g and a positive integer e, we show that
there is a group homomorphism A(k) --> (Z/g(1)Z)^e whose kernel and
cokernel are elementary abelian 2-groups. In particular, this map is
an isomorphism if the characteristic of k is 2 or A is simple of
dimension greater than 2; in the last case one has e=1 or 2, and A(k)
is isomorphic to (Z/g(1)Z)^e.

Hui Zhu <zhu@msri.org>