Linkage of sheaves of modules

TL;DR

This paper generalizes the concept of linkage from modules to sheaves of modules, exploring its properties and construction methods within algebraic geometry.

Contribution

It introduces the linkage of sheaves of modules, demonstrating its local nature and methods to construct maximal linked subsheaves.

Findings

Linkedness of sheaves is a local property.

Sheaves of modules formed by glueing schemes are linked.

Maximal linked subsheaves exist on non-domain sheaves.

Abstract

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of sheaves is a locally property. As an important result, we have shown that the sheaf of modules made of Glueing schemes and Glueing linked sheaves of modules is a linked sheaf. Also, it has been shown that for every sheaf of modules on non-domain, it is possible to obtain a maximal linked subsheaf of modules.