T-structures on dg-categories and derived deformations

TL;DR

This paper develops a framework for understanding infinitesimal derived deformations of pretriangulated dg-categories with t-structures, extending classical deformation theory of abelian categories and linking deformations of dg-categories to their t-structures.

Contribution

It introduces a foundational approach to infinitesimal derived deformation theory for dg-categories with t-structures, generalizing previous work on abelian categories.

Findings

Deformations of dg-categories of derived injectives induce deformations of t-structures.

The framework generalizes classical deformation theory to the derived setting.

Establishes connections between dg-category deformations and t-structure deformations.

Abstract

This paper is a sequel to "t-structures and twisted complexes on derived injectives" by the same authors. We develop the foundations of the infinitesimal derived deformation theory of pretriangulated dg-categories endowed with t-structures. This generalizes the deformation theory of abelian categories developed by the last two authors. We show how deformations of dg-categories of derived injectives yield derived deformations of the associated t-structures.