Title: The inertial Jacquet-Langlands correspondence,
Abstract: We give a parametrization of the simple Bernstein components of inner forms
of a general linear group over a local field by invariants constructed from
type theory, and explicitly describe its behaviour under the Jacquet-Langlands
correspondence. Along the way, we prove a conjecture of Broussous, Sécherre
and Stevens on preservation of endo-classes.