Let A be a supersingular abelian variety deened over a nite eld k. We give an approximate description of the structure of the group A(k) of k-rational points of A in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative to k. Write f = Q gi e i for distinct monic irreducible polynomials gi and positive integers ei, we show that there is a group homomorphism ' : A(k) ?! Q (Z=gi(1)Z) e i that is \almost" an isomorphism in the sense that the size of the kernel and… CONTINUE READING