Mathematics – Number Theory
Scientific paper
1998-08-31
Mathematics
Number Theory
Scientific paper
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.
No associations
LandOfFree
Group structures of elementary supersingular abelian varieties over finite fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Group structures of elementary supersingular abelian varieties over finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Group structures of elementary supersingular abelian varieties over finite fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-503309