Organisateurs: Michel Balazard (CNRS, Laboratoire Poncelet) , Michael Tsfasman (CNRS, Laboratoire Poncelet, Institut des Probl mes de Transmission de l'Information) , Alexey Zykin (Laboratoire Poncelet, Haute Ecole d'Economie) . ... The situation over number fields is almost entirely conjectural, the situation over function fields of finite characteristic is much better. ... The work over function fields is joint with Amilcar Pacheco (Rio, Brazil) . Laboratoire Poncelet . ...