Vendredi 8 avril 2011 à 15h00 en salle C221
Alexey Zaytsev (Claude Shannon Institute and University College Dublin)

Titre : Curves over finite fields with many rational points, existence and constructions

Résumé :
Let C be an irreducible non-singular projective curve over a finite field F_q. It is called "a curve with many rational points" if its number of rational points close to N_g(q), where g is genus of the curve C. In this talk we consider problems of existence and constructions of such curves. In particular, we will overview of varies methods of improvement of the Hasse-Weil bound (analogy of the Riemann hypothesis for curves over finite fields). We will also consider a solution of these problems for genus 1, 2 and a partial solution for genus 3. At the second part of the talk, my improvement of the Hasse-Weil-Serre bound for curves of low genera and some construction of optimal curves of genus 3 over finite fields with certain discriminant will be presented.

Remarques : Attention à l'heure et à la salle !