AKSZ construction for shifted Poisson structures

Fuente: arXiv
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Auteur principal: Tomić, Nikola
Format: Preprint
Publié: 2026
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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