Computing l-isogenies between elliptic curves defined over a finite field F q of small
characteristic is of some importance for the computation of the cardinalities of elliptic curves …

Cette thèse est consacrée au calcul du nombre de points d'une courbe elliptique définie sur
un corps fini. Nous étudions dans une première partie l'algorithme de Schoof et ses …

The well-known analogies between number fields and function fields have led to the
transposition of many problems from one domain to the other. In this paper, we will discuss …

If F is a global function field of characteristic p> 3, we employ Tate's theory of analytic
uniformization to give an alternative proof of a theorem of Igusa describing the image of the …

The problem of computing an explicit isogeny between two given elliptic curves over Fq,
originally motivated by point counting, has recently awaken new interest in the cryptology …

We prove that the local height of a point on a Drinfeld module can be computed by
averaging the logarithm of the distance to that point over the torsion points of the module …

1. Introduction. Let A be an abelian variety over a function field K in one variable over a finite
field k. Let v be a place of K. In this paper we will study the topology induced on A (K) by the …

Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to
obtain definability and decidability results of large classes of infinite algebraic extensions of …

The purpose of this paper is to survey some of the recent finiteness results on rational and
integral points on algebraic varieties defined over global fields of positive characteristics. In …

Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to
obtain definability and decidability results of large classes of infinite algebraic extensions of …