On the local semi-simplicity of ordinary modular Galois representations
(Un exposé d'Eknath Ghate au séminaire de
théorie des nombres de Chevaleret le 5 avril 2004)
Résumé :
Let $f$ be a $p$-ordinary primitive cusp form
of weight at least 2. Then the restriction
to a decomposition group at $p$ of the two
dimensional $p$-adic Galois representation
attached to $f$ is upper-triangular. When
$f$ has complex multiplication it is not
hard to see that it is even diagonal. In this
talk we will provide some evidence which shows that
the converse also holds. This is joint work
with Vinayak Vatsal.