Sur la cohomologie de certains espaces de modules de fibr\'es vectoriels

Abstract

Let M be a moduli space of stable vector bundles on a curve with rank and degree fixed and coprime. We give a simple proof that the rational cohomology of M is generated by the Kunneth components of the Chern classes of the universal bundle. The proof applies also to some moduli spaces of vector bundles over higher-dimensional varieties.