| Résume | The Fontaine-Mazur conjecture predicts that 2-dimensional p-adicGaloisrepresentations, whose restriction to a decomposition group at p satisfiesa certaincondition (potential semi-stability), come from modular forms.I will explain a result which says that if a representation satisfiesthisconditionand comes from an overconvergent modular form, then it comes from aclassical modular form.This is significant, because overconvergent modular forms are very closelyrelatedto classical ones. The fact that the potential semi-stability conditioncan distinguishbetween classical and non-classical forms, therefore provides a goodtestof the conjecture. |
