Analytic and algebraic integrability of quasi-smooth derived foliations

Abstract: We study integrability results for derived foliations in the holomorphic context. We prove a global integrability theorem by flat groupoids, as well as global algebraic integrability in the presence of a compact leaf with finite holonomy groups. These results are generalization to the derived (and thus singular) setting of well know results and constructions: integration of holomorphic foliations by smooth groupoid and global stability in the holomorphic situation.