The primitive spectrum of C^*-algebras of \'etale groupoids with abelian isotropy

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