  Given a Hausdorff locally compact \'etale groupoid $\mathcal G$, we describe
as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$
obtained by inducing one-dimensional representations of amenable isotropy
groups of $\mathcal G$. When $\mathcal G$ is amenable, second countable, with
abelian isotropy groups, our result gives the description of
$\operatorname{Prim} C^*(\mathcal G)$ 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.
