Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties

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.