Sur un problème de compatibilité local-global localement analytique

Abstract

We reinterpret a conjecture of Breuil on the locally analytic ${\mathrm{Ext}}^1$ in a functorial way using $(\phi ,\Gamma )$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this "improved" conjecture, notably for ${\mathrm{GL}}_3({\mathbb{Q}}_p)$.

157 pages, in French