Local cohomology of graded rings and projective schemes
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.
local cohomology groups of graded modules
local cohomology groups of quasi-coherent sheaves
scientific article; zbMATH DE number 4179509
scientific article