Towards the Derived Jacquet-Emerton Module Functor

Abstract

Let $G$ be a $p$-adic Lie group associated to a connected reductive group over ${\mathbb{Q}}_p$. Let $P$ be a parabolic subgroup of $G$ and let $M$ be a Levi quotient of $P$. In this paper, we define a $\delta$-functor $H^{\star }{J}_P$ from the category of admissible locally analytic $G$-representations to the category of essentially admissible locally analytic $M$-representations that extends the Jacquet-Emerton module functor $J_P$ defined by Emerton.

Any comments are welcomed!