Affinoid Quillen's Lemma and its applications

Let $k$ be a field and $A$ a $k$-algebra. The classical Quillen's Lemma states that if $A$ if is equipped with an exhaustive filtration such that the associated graded ring is commutative and finitely generated $k$-algebra then for any finitely generated $A$-module $M$, every element of the endomorphism ring of $M$ is algebraic over $k$. In particular, Quillen's Lemma may be applied to the enveloping algebra of a finite dimensional Lie algebra. I aim to present an affinoid version of Quillen's Lemma which strengthness a theorem proved by Ardakov and Wadsley. Depending on time, I will show how this leads to an (almost) classification of the primitive spectrum of the affinoid enveloping algebra of a semisimple Lie algebra.