Torsion functors with monomial support

TL;DR

This paper explores how torsion functors depend on their supporting ideals, focusing on monomial ideals in subrings of polynomial algebras, and relates flatness of sheaves on toric schemes to graded local cohomology.

Contribution

It provides new insights into the relationship between torsion functors, monomial ideals, and flatness of sheaves on toric schemes, extending understanding in non-Noetherian contexts.

Findings

Torsion functors' dependence on monomial support is characterized.

Connections between flatness of quasicoherent sheaves and graded local cohomology are established.

Results apply to subrings of polynomial algebras over general rings.

Abstract

The dependence of torsion functors on their supporting ideals is investigated, especially in the case of monomial ideals of certain subrings of polynomial algebras over not necessarily Noetherian rings. As an application it is shown how flatness of quasicoherent sheaves on toric schemes is related to graded local cohomology.