Normal forms of $\mathbb{Z}$-graded $Q$-manifolds

Following recent results of A.K. and V.S. on $\mathbb{Z}$-graded manifolds, we give several local and global normal forms results for $Q$-structures on those, i.e. for differential graded manifolds. In particular, we explain in which sense their relevant structures are concentrated along the zero-locus of their curvatures, especially when the negative part is of Koszul–Tate type. We also give a local splitting theorem.