Strictification and gluing of Lagrangian distributions on derived schemes with shifted symplectic forms

Abstract

A strictification result is proved for isotropic distributions on derived schemes equipped with negatively shifted homotopically closed $2$-forms. It is shown that any derived scheme over $\mathbb{C}$ equipped with a $-2$-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg ${\mathbb{C}}^{\infty }$-manifold.

35 pages, updated the title of the article and the abstract, added fixations and content to main body of the article and improved some of the proofs. We appreciate any comments