On the group orders of elliptic curves over finite fields
Bounds on polarizations of abelian varieties over finite fields.
The Weil pairing and the Hilbert symbol.
Corrigendum to: Improved upper bounds for the number of points on curves over finite fields
Improved upper bounds for the number of points on curves over finite fields
We give new arguments that improve the known upper bounds on the maximal number of rational points of a curve of genus over a finite field , for a number of pairs . Given a pair and an integer , we determine the possible zeta functions of genus- curves over with points, and then deduce properties of the curves from their zeta functions. In many cases we can show that a genus- curve over with points must have a low-degree map to another curve over , and often this is enough to...
Jacobians in isogeny classes of abelian surfaces over finite fields
We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus- curves over finite fields.
Page 1