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

Abstract

Let $\mathbf{C}$ be a smooth geometrically connected projective curve over a finite field, and let $A$ be the affine algebra of its regular functions outside a fixed place of $\mathbf{C}$. We give precise relationships between the Mahler successive minima of normed $A$-lattices and the Harder-Narasimhan slopes of vector bundles over $\mathbf{C}$ using their category equivalence.

22 pages, in French language, 2 figures