A Quillen Model Structure Approach to the Finitistic Dimension Conjectures

TL;DR

This paper introduces a novel model category framework to study the Finitistic Dimension Conjectures, connecting module classes with finite imensionality to homotopical algebra.

Contribution

It develops a new model structure approach to analyze the Finitistic Dimension Conjectures, providing a fresh conceptual framework for their investigation.

Findings

Established a model structure for modules with finite imensionality

Provided new insights into the Finitistic Dimension Conjectures

Proposed a homotopical perspective on longstanding conjectures

Abstract

We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the Finitistic Dimension Conjectures and present a new conceptual framework in which these conjectures can be studied.