We introduce and study the derived moduli stack $mathrm{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on $X$, we prove that $mathrm{Symp}(X, n)$ carries a canonical shifted quadratic form. This generalizes a classical result of Fricke and Habermann, which was established in the $C^{infty}$-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated by Vezzosi.
The derived moduli stack of shifted symplectic structures
Valerio Melani
2019-01-01
Abstract
We introduce and study the derived moduli stack $mathrm{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on $X$, we prove that $mathrm{Symp}(X, n)$ carries a canonical shifted quadratic form. This generalizes a classical result of Fricke and Habermann, which was established in the $C^{infty}$-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated by Vezzosi.File in questo prodotto:
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