GAGA for DQ-Algebroid

Abstract

Let $X$ be a smooth complex projective variety with associated compact manifold $X_{\mathrm{an}}$. If ${\mathcal{A}}_X$ is a DQ-algbroid on $X$, then there is an induced DQ-algebroid ${\mathcal{A}}_{X_{\mathrm{an}}}$ on $X_{\mathrm{an}}$. We show that the natural functor from the derived category of bounded complexes of ${\mathcal{A}}_X$-modules with coherent cohomologies to the derived category of bounded complexes of ${\mathcal{A}}_{X_{\mathrm{an}}}$-modules with coherent cohomologies is an equivalence.