A framework for torsion theory computations on elliptic threefolds

TL;DR

This paper develops a topological and homological algebra framework to analyze torsion pairs in the category of coherent sheaves on elliptic threefolds, recovering known results and establishing new ones.

Contribution

It introduces a novel approach using only topology and homological algebra to study torsion theory on elliptic threefolds, providing new insights and results.

Findings

Recovered existing results on torsion pairs

Proved new results in the category of coherent sheaves

Established a framework based solely on topology and homological algebra

Abstract

We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new results on torsion pairs in the category of coherent sheaves on an elliptic threefold.