  In this paper we treat Grothendieck Duality for noetherian rings via rigid
dualizing complexes. In particular, we prove that every ring, essentially
finite type over a regular base ring, has a unique rigid dualizing complex. The
rigid dualizing complexes have strong functorial properties, allowing us to
construct the twisted induction pseudofunctor, which is our ring-theoretic
version of the twisted inverse pseudofunctor $f^{!}$. This is the first article
of a bigger project, whose final goal is establishing Grothendieck Duality,
including global duality for proper maps, for Deligne-Mumford stacks.
