Resumen de Deformation quantisation for unshifted symplectic structures on derived Artin stacks
J.P. Pridham
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.
