The derived moduli stack of shifted symplectic structures

We introduce and study the derived moduli stack Symp.X; n/ of n-shifted symplectic structures on a given derived stack X, as introduced in [8]. In particular, under reasonable assumptions on X, we prove that Symp.X; n/ carries a canonical quadratic form, in the sense of [14]. This generalizes a classical result of Fricke and Habermann (see [3]), which was established in the C1-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated in [14].