Finite locally free group schemes in characteristic p and Dieudonné modules.
Formal Groups Attached to Elliptic Modular Forms
Forme normale d'une fonction sur une surface de caractéristique positive
Formules explicites pour le nombre de points des variétés sur un corps fini.
Free pencils on divisors.
Frobenius indices of certain curves over finite fields.
Generic Zariski surfaces
Geography for surfaces of general type in positive characteristic.
Global function fields with many rational places over the quinary field. II
Greatest common divisors of , in positive characteristic and rational points on curves over finite fields
In our previous work we proved a bound for the , for -units of a function field in characteristic zero. This generalized an analogous bound holding over number fields, proved in [3]. As pointed out by Silverman, the exact analogue does not work for function fields in positive characteristic. In the present work, we investigate possible extensions in that direction; it turns out that under suitable assumptions some of the results still hold. For instance we prove Theorems 2 and 3 below, from...
Groupes de Chow et K-théorie de variétés sur un corps fini.
Hasse-Witt matrices and Kummer extension
A simple calculation of the Hasse-Witt matrix is used to give examples of curves which are Kummer coverings of the projective line and which have easily determined p-rank. A family of curve carrying non-classical vector bundles of rank 2 is also given.
Hasse-Witt Matrices of Fermat curves.
H*(C/B,L) for G of semi-simple rank 2
Hilbert sets and zeta functions over finite fields.
Hyperelliptic Curves with zero Hasse-Witt-Matrix.
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.
Kloosterman sums and the p-torsion of certain Jacobians.
Kloosterman sums as algebraic integers.