Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles
Abstract
We formulate a notion of quantisation of -Poisson structures on derived Artin -stacks, and construct a map from quantisations of -shifted symplectic structures to power series in de Rham cohomology. For a square root of the dualising line bundle, this gives an equivalence between even power series and self-dual quantisations. In particular, there is a canonical quantisation of any such square root, which localises to recover the perverse sheaf of vanishing cycles on derived DM stacks, thus giving a form of derived categorification of Donaldson--Thomas invariants.
Keywords
Cite
@article{arxiv.1508.07936,
title = {Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:1508.07936},
year = {2019}
}
Comments
34 pp; v2 Artin details added, some material moved to arXiv:1504.01940; v3 several additions and corrections, notably in 1.2.1; v4 some details added and small corrections; v5 minor changes, to appear in Algebraic Geometry