Deformation quantisation for unshifted symplectic structures on derived Artin stacks

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Abstract

We construct a map from DQ algebroid quantisations of unshifted symplectic structures on a derived Artin N-stack to power series in de Rham cohomology, depending only on a choice of Levi decomposition for the Grothendieck--Teichmueller group. This gives an equivalence between even power series and certain involutive quantisations, which yield involutive curved A-infinity deformations of the dg category of perfect complexes. In particular, there is a canonical quantisation associated to every symplectic structure on such a stack, which agrees for smooth varieties with the Kontsevich--Tamarkin quantisation.
Original languageEnglish
Pages (from-to)3027-3059
Number of pages33
JournalSelecta Mathematica (New Series)
Volume24
Issue number4
Early online date27 Apr 2018
DOIs
Publication statusPublished - Sep 2018

Keywords

  • math.AG
  • math.QA

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