A $t$-structure on the $\infty$-category of mixed graded modules

TL;DR

This paper develops a $t$-structure on the $mbda$-category of mixed graded modules over a ring of characteristic zero, linking it to filtered modules and providing foundational results for future research.

Contribution

It introduces a new $t$-structure on mixed graded modules and relates it to the Beilinson $t$-structure, offering a model-independent framework.

Findings

Established a left and right complete accessible $t$-structure.

Identified the $mbda$-category of mixed graded modules with the left completion of the Beilinson $t$-structure.

Provided foundational results for future work in the area.

Abstract

In this work, we shall study in a purely model-independent fashion the $\infty$-category of mixed graded modules over a ring of characteristic $0$, and collect some basic results about its main formal properties. Finally, we shall endow such $\infty$-category with a both left and right complete accessible $t$-structure, showing how this identifies the $\infty$-category of mixed graded modules with the left completion of the Beilinson $t$-structure on the \infinity-category of filtered modules. Most of the content of this paper is already available in literature, and it serves mainly as a reference for future work.