Shifted Lagrangian thickenings of shifted Poisson derived schemes

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Tomić, Nikola
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915866214400000
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