Supersingular Abelian Varieties over Finite Fields
نویسنده
چکیده
Let A be a supersingular abelian variety defined over a finite field 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 = > gi i for distinct monic irreducible polynomials gi and positive integers ei . We show that there is a group homomorphism .: A(k) > (Z gi (1) Z)i that is ``almost'' an isomorphism in the sense that the sizes of the kernel and the cokernel of . are bounded by an explicit function of dim A. 2001 Academic Press 1991 Mathematics Subject Classifications: Primary 11G15; Secondary 14G10, 11N37.
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تاریخ انتشار 2001