| Résume | We consider representations of $GL_n(F)$, where $F$ is a $p$-adic field, over $l$-adic coefficient rings for $l$ not equal to $p$. The points of the coefficient ring parametrize a family of representations. We discuss the question of attaching Rankin-Selberg local Euler factors to certain admissible generic families in way that interpolates the classical local factors at each point, as well as their functional equation and gamma factor. With remaining time we discuss the relationship to the conjectural local Langlands correspondence in families of Emerton-Helm. |
