Tame Loci of Certain Local Cohomology Modules
Markus Brodmann, Maryam Jahangiri

TL;DR
This paper investigates the tame loci of local cohomology modules of graded modules over Noetherian rings, focusing on primes of height up to three, to understand their structural properties in algebraic geometry.
Contribution
It introduces the concept of tame loci at level i in codimension ≤ 3 for local cohomology modules, providing new insights into their behavior over graded rings.
Findings
Characterization of tame loci in codimension ≤ 3.
Identification of conditions for tameness of local cohomology modules.
Structural properties of local cohomology modules in specific codimensions.
Abstract
Let be a finitely generated graded module over a Noetherian homogeneous ring . For each let denote the -th local cohomology module of with respect to the irrelevant ideal of , furnished with its natural grading. We study the tame loci at level in codimension of , that is the sets of all primes of height such that the graded -modules are tame.
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