Resumen

Periodic cyclic homology plays for noncommutative spaces the role of de Rham cohomology in the commutative setting. After a brief review of its developments, from the Cuntz-Quillen approach to the group-equivariant theory, we describe a module-theoretic framework in which we build the main objects of the talk. In particular, we work in the category of essential modules over the Steinberg algebra of an ample groupoid. Within this setting, we present the definition of bivariant equivariant periodic cyclic homology for groupoid actions. Finally, we discuss its basic features: homotopy invariance, stability, excision, and a result in the spirit of the Green-Julg theorem for actions of proper groupoids.