Local cohomology of graded rings and projective schemes
type: Item
instance of: scholarly article
title: Local cohomology of graded rings and projective schemes
zbMATH Open document ID: 0716.13012
DOI: 10.1016/0022-4049(89)90032-7
author: Alain Verschoren
author: J. L. Bueso
author: Blas Torrecillas
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The main result of the paper expresses the local cohomology groups of quasi-coherent sheaves on Proj(R) with support in an arbitrary subset as the local cohomology groups of graded R-modules with respect to a suitable choosen idempotent kernel functor in the category of graded R- modules (see 2.5, 2.8, 3.8, 3.10, having 2 proofs, 3.13 which can be viewed as a geometric realization of the graded local cohomology modules introduced in 3.1). Some difficulties encounter since R is not necessarily noetherian and quasi-coherent sheaves on Proj(R) and graded R-modules do not uniquely determine each other.
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 4179509
zbMATH Keywords: local cohomology groups of graded modules
zbMATH Keywords: local cohomology groups of quasi-coherent sheaves
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90032-7
OpenAlex ID: W2094740603
cites work: Q4093555
cites work: Some aspects of non-noetherian local cohomology
cites work: Q3929853
cites work: Relating homological dimensions to relative homological dimensions
cites work: Torsion Theory and Associated Primes
cites work: Commutative Torsion Theory
cites work: Rings and modules of quotients
cites work: On graded rings. I
cites work: Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne
cites work: Q4143433
cites work: Graded and filtered rings and modules
cites work: Q4049223
cites work: Localization of sheaves and Cousin complexes
cites work: Q5541099
cites work: Q3222350
cites work: Fully bounded Grothendieck categories. II: Graded modules
cites work: Q4195084
cites work: On the Brauer group of a projective variety
cites work: Q3778858
cites work: Local cohomology and quasicoherent sheaves
description: scientific article; zbMATH DE number 4179509