AKSZ construction for shifted Poisson structures
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915715249864704 |
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| author | Tomić, Nikola |
| author_facet | Tomić, Nikola |
| contents | We prove the AKSZ theorem for shifted Poisson structures: if $X$ is an $n$-shifted Poisson derived stack, and $Y$ a $d$-oriented derived stack, then the mapping stack \[\underline{\mathrm{Map}}(Y,X)\] is naturally endowed with an $(n-d)$-shifted Poisson structure. For this, we prove that the data of an $n$-shifted Poisson structure on a derived Artin stack is equivalent to the data of an $(n+1)$-shifted Lagrangian thickening of it. We also extend the definition of shifted Poisson structures to derived prestacks having a deformation theory and give two applications, one for mapping stacks with a non-proper source and one in BV formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | AKSZ construction for shifted Poisson structures Tomić, Nikola Algebraic Geometry Algebraic Topology We prove the AKSZ theorem for shifted Poisson structures: if $X$ is an $n$-shifted Poisson derived stack, and $Y$ a $d$-oriented derived stack, then the mapping stack \[\underline{\mathrm{Map}}(Y,X)\] is naturally endowed with an $(n-d)$-shifted Poisson structure. For this, we prove that the data of an $n$-shifted Poisson structure on a derived Artin stack is equivalent to the data of an $(n+1)$-shifted Lagrangian thickening of it. We also extend the definition of shifted Poisson structures to derived prestacks having a deformation theory and give two applications, one for mapping stacks with a non-proper source and one in BV formalism. |
| title | AKSZ construction for shifted Poisson structures |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2601.04064 |