Title: The primitive spectrum of C$^*$-algebras of étale groupoids with abelian isotropy

Abstract: Given a Hausdorff locally compact \'etale groupoid $\G$, we describe as a topological space the part of the primitive spectrum of $C^*(\G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of $\G$. When $\G$ is amenable, second countable, with abelian isotropy groups, our result gives the description of $\Prim C^*(\G)$ conjectured by Van~Wyk and Williams. This, in principle, completely determines the ideal structure of a large class of separable C$^*$-algebras, including the transformation group C$^*$-algebras defined by amenable actions of discrete groups with abelian stabilizers and the C$^*$-algebras of higher rank graphs.