TL;DR
This paper investigates conditions under which graded local cohomology commutes with coarsening functors, providing criteria and an example where it fails to do so.
Contribution
It establishes new criteria for the commutation of graded local cohomology with coarsening and presents a counterexample demonstrating non-commutation.
Findings
Criteria for commutation are proven.
An explicit example of non-commutation is provided.
The study advances understanding of graded local cohomology behavior.
Abstract
Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.
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