Title: Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties
Authors: Mattia Ornaghi, Saurabh Singh and Amnon Yekutieli
Publication status:
Eprint https://arxiv.org/abs/2402.07150 (2024)
Abstract: 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.
updated 14 Feb 2024