Integral representation theorems for DQ-modules

Abstract

We identify the type of $\mathbb{C}[[\hslash ]]$-linear structure inherent in the $\infty$-categories which arise in the theory of Deformation Quantization modules. Using this structure, we show that the $\infty$-category of quasicoherent cohomologically complete DQ-modules is a deformation of the $\infty$-category of quasicoherent sheaves. We also obtain integral representation results for DQ-modules similar to the ones of Toën and Ben-Zvi-Nadler-Francis, stating that suitably linear functors between $\infty$-categories of DQ-modules are integral transforms.

41 pages

References in corpus (1)

• Higher Topos Theory