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A Darboux theorem for derived schemes with shifted symplectic structure

Abstract:

We prove a 'Darboux theorem' for derived schemes with symplectic forms of degree $k<0$, in the sense of Pantev, Toen, Vaquie and Vezzosi arXiv:1111.3209. More precisely, we show that a derived scheme $X$ with symplectic form $\omega$ of degree $k$ is locally equivalent to (Spec $A,\omega'$) for Spec $A$ an affine derived scheme whose cdga $A$ has Darboux-like coordinates in which the symplectic form $\omega'$ is standard, and the differential in $A$ is given by Poisson bracket with a Hamil...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1090/jams/910

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Lincoln College; Lincoln College
ORCID:
0000-0002-3530-8801
Publisher:
American Medical Society Publisher's website
Journal:
Journal of the American Mathematical Society Journal website
Volume:
32
Pages:
399-443
Publication date:
2018-10-01
Acceptance date:
2018-08-29
DOI:
EISSN:
1088-6834
ISSN:
0894-0347
Pubs id:
pubs:401038
URN:
uri:44a257f5-31ef-45ae-9edb-4305c9dcf3b8
UUID:
uuid:44a257f5-31ef-45ae-9edb-4305c9dcf3b8
Local pid:
pubs:401038
Keywords:

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