Filtered moment graph sheaves

TL;DR

This paper introduces (co-)filtered sheaves on quotient moment graphs, extending canonical sheaves, and demonstrates that their global sections form indecomposable projective objects in a new exact category.

Contribution

It develops a (co-)filtered framework for moment graph sheaves and identifies their global sections as indecomposable projectives, advancing the algebraic understanding of these structures.

Findings

Global sections of filtered sheaves are indecomposable projectives.

Extension of canonical sheaves to filtered versions.

Establishment of a new exact category for these sheaves.

Abstract

We introduce the notion of (co-)filtered sheaves on quotients of moment graphs by a group action. We then introduce a (co-)filtered version of the canonical sheaves of Braden and MacPherson and show that their global sections are the indecomposable projective objects in a suitably defined exact category.