Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles

J. P. Pridham

doi:10.14231/AG-2019-032

Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles

J. P. Pridham

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We construct a map from E_0 quantisations of (-1)-shifted symplectic structures to power series in de Rham cohomology of derived Artin N-stacks. 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 cycle on derived DM stacks.

Original language	English
Pages (from-to)	747-779
Number of pages	33
Journal	Algebraic Geometry
Volume	6
Issue number	6
DOIs	https://doi.org/10.14231/AG-2019-032
Publication status	Published - 30 Nov 2019

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math.AG

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10.14231/AG-2019-032

1508.07936v3Submitted manuscript, 303 KB
DQvanishpapAccepted author manuscript, 465 KBLicence: Creative Commons: Attribution Non-Commercial (CC-BY-NC)

Jon Pridham
- School of Mathematics - Personal Chair of Derived Algebraic Geometry
Person: Academic: Research Active

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AB - We construct a map from E_0 quantisations of (-1)-shifted symplectic structures to power series in de Rham cohomology of derived Artin N-stacks. 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 cycle on derived DM stacks.

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Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles

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Jon Pridham

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