Description
Using a going-down principle, Chabert, Echterhoff and Oyono-Oyono proved the injectivity of the assembly map for locally compact Hausdorff groups that are amenable at infinity. Bönicke proved the analogue for ample groupoids. In this talk we present the proof of the going-down principle for étale groupoids in general. It yields the injectivity of the assembly map for étale groupoids that are strongly amenable at infinity, which was firstly proved by Bönicke and Proietti via a categorical approach.
