Noncommutative supports, local cohomology and spectral sequences
Abstract
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or strongly locally noetherian. Using what we call elementary objects and their injective hulls, we develop a theory of supports and associated primes in these categories. We apply our theory to study a general functorial setup that requires certain conditions on the injective hulls of elementary objects and gives us spectral sequences for derived functors associated with local cohomology objects, as well as generalized local cohomology and also generalized Nagata ideal transforms.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of Noncommutative Geometry
- Volume
- 20
- Issue
- 4
- Pages
- 1197–1224
- Publication date
- 26 August 2026
- Language
- EN