2024/02/11 by Mattia Ornaghi, Ornaghi, Mattia, Saurabh Kumar Singh +3
Mathematics · #13D09 #16E45 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 14F08. Secondary: 18G80 #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2402.07150
openalex publication_date 2024/02/11 · openalex created_date 2024/02/14 · openalex updated_date 2026/07/28
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.