Group Structures of Elementary Supersingular Abelian Varieties over Finite Fields
نویسنده
چکیده
Let A be a supersingular abelian variety over a finite field k which is k-isogenous to a power of a simple abelian variety over k. Write the characteristic polynomial of the Frobenius endomorphism of A relative to k as f = g for a monic irreducible polynomial g and a positive integer e. We show that the group of k-rational points A(k) on A is isomorphic to (Z g(1) Z) unless A's simple component is of dimension 1 or 2, in which case we prove that A(k) is isomorphic to (Z g(1) Z)_ (Z (g(1) 2) Z_Z 2Z) for some non-negative integers a, b with a+b=e. In particular, if the characteristic of k is 2 or A is simple of dimension greater than 2, then A(k)$(Z g(1) Z). 2000 Academic Press
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Supersingular Abelian Varieties over Finite Fields
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