The Codimension-Three conjecture for holonomic DQ-modules

TL;DR

This paper proves a conjecture about the extension of holonomic DQ-modules across subsets of codimension three or more, generalizing a known result for microdifferential modules.

Contribution

It establishes a codimension-three extension property for holonomic DQ-modules, extending the analogy with microdifferential modules proved by Kashiwara and Vilonen.

Findings

Holonomic DQ-modules with a lattice extend uniquely across codimension ≥3 subsets.

The result generalizes the codimension-three conjecture to DQ-modules.

Provides a new tool for analyzing the structure of DQ-modules in complex geometry.

Abstract

We prove an analogue for holonomic DQ-modules of the codimension-three conjecture for microdifferential modules recently proved by Kashiwara and Vilonen. Our result states that any holonomic DQ-module having a lattice extends uniquely beyond an analytic subset of codimension equal to or larger than three in a Lagrangian subvariety containing the support of the DQ-module.