On the conjecture of Lichtenbaum and of Chinburg over function fields.
On the Converse of Abel's Theorem in Characteristic p.
On the discrete logarithm problem for plane curves
In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of , where is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number the following holds: We consider the discrete logarithm problem for curves given by plane models...
On the distribution of the Fₚ-points on an affine curve in r dimensions
On the dual variety in characteristic 2
On the existence of supersingular curves of given genus.
On the Finite Field Nullstellensatz for the intersection of two quadric hypersurfaces.
On the Gauss maps of space curves in characteristic p
On the Gauss maps of space curves in characteristic p, II
On the generic injectivity of the Gauss map in positive characteristic.
On the group of components of a Néron model.
On the group orders of elliptic curves over finite fields
On the Hodge-Tage decomposition in the imperfect residue field case.
On the Holomorphy on Certain Non-Abelian L-Series.
On the moduli of quasi-canonical liftings
On the Normal Bundles of Rational Space Curves.
On the number of points on abelian and Jacobian varieties over finite fields
We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.
On the p-rank of an abelian variety and its endomorphism algebra.
Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End0(A). As is well known, End0(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative field. Nevertheless, we give an example...
On the values of the zeta function of a variety over a finite field
On the zeta function of a complete intersection