Fonctions zêta des hauteurs des espaces fibrés

Fonction zêta des hauteurs des variétés toriques non déployées

We investigate 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 give a detailed account of their method.

全局函数域上网络的逐次极小值与向量丛的斜率

Minima successifs des réseaux et pentes des fibrés vectoriels sur les corps de fonctions globaux

本文利用范畴等价，给出了赋范 $A$-格的 Mahler 逐次极小值与有限域上射影曲线 ${\f C}$ 上向量丛的 Harder-Narasimhan 斜率之间的精确关系。

Conjectures sur les dérivées logarithmiques des fonctions L d'Artin aux entiers négatifs

We formulate several variants of a conjecture relating the arithmetic degree of certain hermitian fibre bundles with the values of the logarithmic derivative of Artin's L-functions at negative integers. This generalizes conjectures by Colmez and Gross-Deligne and complements Beilinson's conjectures for the Artin motives. We announce several results in the direction of these statements.

Sur le rang des Jacobiennes sur un corps de fonctions

On the rank of Jacobians over function fields.} Let $f:\mathcal{X}\to C$ be a projective surface fibered over a curve and defined over a number field $k$. We give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the jacobian of the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of $f$. The results also give a reinterpretation of the Tate conjecture for the surface $\mathcal{X}$ and generalizes results of Nagao, Rosen-Silverman and Wazir.