On supersingular abelian varieties of dimension two over finite fields
Let \(A\) be an abelian variety over a finite field \(k\) of characteristic \(p>0\). The fact that \(A\) is supersingular, i.e. the group of \(p\)-torsion points on \(A\) is trivial, can be expressed in terms of the characteristic polynomial of the Frobenius endomorphism of \(A\) over the finite field \(k\). The author gives a list of all these characteristic polynomials for supersingular abelian varieties \(A\) of dimension 2. In addition he shows which of these abelian varieties are isogenous to Jacobians of curves. Then he studies the group structure of the \(k\) rational points \(A(k)\) in these cases.
scientific article; zbMATH DE number 1144295