Shifted Lagrangian thickenings of shifted Poisson derived schemes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915866214400000 |
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| author | Tomić, Nikola |
| author_facet | Tomić, Nikola |
| contents | We prove that the space of shifted Poisson structures on a derived scheme $X$ locally of finite presentation is equivalent to the space of shifted Lagrangian thickenings out $X$, solving a conjecture in shifted Poisson geometry. As a corollary, we show that for $M$ a compact oriented $d$-dimensional manifold and an $n$-shifted Poisson structure on $X$, the mapping stack $\mathrm{Map}(M,X)$ has an $(n-d)$-shifted Poisson structure. It extends a known theorem for shifted symplectic structures to shifted Poisson structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shifted Lagrangian thickenings of shifted Poisson derived schemes Tomić, Nikola Algebraic Geometry Algebraic Topology Symplectic Geometry We prove that the space of shifted Poisson structures on a derived scheme $X$ locally of finite presentation is equivalent to the space of shifted Lagrangian thickenings out $X$, solving a conjecture in shifted Poisson geometry. As a corollary, we show that for $M$ a compact oriented $d$-dimensional manifold and an $n$-shifted Poisson structure on $X$, the mapping stack $\mathrm{Map}(M,X)$ has an $(n-d)$-shifted Poisson structure. It extends a known theorem for shifted symplectic structures to shifted Poisson structures. |
| title | Shifted Lagrangian thickenings of shifted Poisson derived schemes |
| topic | Algebraic Geometry Algebraic Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2506.23348 |