We prove that every 0-shifted symplectic structure on a derived Artin
n-stack admits a curved A∞ deformation quantisation. The classical
method of quantising smooth varieties via quantisations of affine space does
not apply in this setting, so we develop a new approach. 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 Drinfeld associator. This gives an equivalence between even power
series and certain involutive quantisations, which yield anti-involutive curved
A∞ 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 for even associators.Comment: 27pp.; v2 Propositions 1.23 and 3.10 added; v3 several small
additions; v4 several changes following referee's comments, to appear in
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