DG Affinity of DQ-modules

TL;DR

This paper proves the dg affinity of formal deformation algebroid stacks on complex smooth algebraic varieties by introducing a new triangulated category of cohomologically complete modules with quasi-coherent graded modules.

Contribution

It introduces a novel triangulated category for formal deformation modules and establishes their dg affinity on complex algebraic varieties.

Findings

Proves dg affinity of formal deformation algebroid stacks.

Defines a new triangulated category of cohomologically complete modules.

Shows the associated graded modules are quasi-coherent.

Abstract

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically complete and whose associated graded module is quasi-coherent.