The derived moduli stack of shifted symplectic structures

  • Samuel Bach

    University of British Columbia, Vancouver, Canada
  • Valerio Melani

    Università di Pisa, Italy and Università di Milano, Italy
The derived moduli stack of shifted symplectic structures cover
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Abstract

We introduce and study the derived moduli stack Symp(X,n)\mathbf {Symp}(X,n) of nn-shifted symplectic structures on a given derived stack XX, as introduced in [8]. In particular, under reasonable assumptions on XX, we prove that Symp(X,n)\mathbf {Symp}(X,n) carries a canonical quadratic form, in the sense of [14]. This generalizes a classical result of Fricke and Habermann (see [13]), which was established in the CC^{\infty}-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated in [14].

Cite this article

Samuel Bach, Valerio Melani, The derived moduli stack of shifted symplectic structures. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 221–241

DOI 10.4171/RSMUP/24