Constante de Peyre des variétés toriques en caractéristique positive
Résumé
We compute the anticanonical height zeta function of a (non necessarily split) toric variety defined over a global field of positive characteristic, drawing our inspiration from the method used by Batyrev and Tschinkel to deal with the analogous problem over a number field. By the way, we recall a sketch of their method. One of the difficulties inherent to the functional case is the more delicate interpretation of the main term of the height zeta function. In fact, by combining the formula we obtain with a recent result of Colliot-Thélène and Suresh, we see that the known conjectural interpretation of the main term is not valid for every toric variety defined over a global field of positive characteristic, contrarily to what happens over a number field.