Deformation quantisation for unshifted symplectic structures on derived Artin stacks
Abstract
We prove that every -shifted symplectic structure on a derived Artin -stack admits a curved 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 -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 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.
Cite
@article{arxiv.1604.04458,
title = {Deformation quantisation for unshifted symplectic structures on derived Artin stacks},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:1604.04458},
year = {2018}
}
Comments
27pp.; v2 Propositions 1.23 and 3.10 added; v3 several small additions; v4 several changes following referee's comments, to appear in Selecta