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Strictification and gluing of Lagrangian distributions on derived schemes with shifted symplectic forms

Advances in Mathematics. 2024. Vol. 438. Article 109477.
Borisov D., Sheshmani A., Yau S., Katzarkov Ludmil

A strictification result is proved for isotropic distributions on dg schemes equipped with −2-shifted homotopically closed 2-forms. Then it is shown that any dg scheme over C equipped with a −2-shifted symplectic structure, when considered as a dg C∞-manifold,, admits a globally defined derived foliation that is Lagrangian with respect to the imaginary and negative definite with respect to the real parts of the −2-shifted symplectic structure.

Research target: Mathematics
Language: English
DOI
Keywords: shifted symplectic structures
Publication based on the results of:
Geometric, categorical and automorphic methods in mirror symmetry and mathematical physics (2024)
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