A Derived Legendrian Category for Shifted Contact Stacks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910253314998272 |
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| author | İzbudak, Efe Berktav, Kadri İlker |
| author_facet | İzbudak, Efe Berktav, Kadri İlker |
| contents | We construct the derived Legendrian category $\mathcal{F}_{c}(X)$ for an $n$-shifted contact derived Artin stack $X$ and the $(\infty,2)$-category $Leg_n$ of Legendrian correspondences in the context of derived algebraic geometry, with several applications to moduli theory. In brief, the objects of the category $\mathcal{F}_{c}(X)$ are Legendrian morphisms; the morphism spaces and composition operations are defined using equivariant descent. We also establish that $\mathcal{F}_{c}(X)$ embeds into an $(\infty, 2)$-category of spans defined by the AKSZ construction. We further evaluate topological cobordisms as Lagrangian correspondences to define derived Legendrian surgery. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13792 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Derived Legendrian Category for Shifted Contact Stacks İzbudak, Efe Berktav, Kadri İlker Algebraic Geometry Symplectic Geometry 14A20, 14A30, 14F08 We construct the derived Legendrian category $\mathcal{F}_{c}(X)$ for an $n$-shifted contact derived Artin stack $X$ and the $(\infty,2)$-category $Leg_n$ of Legendrian correspondences in the context of derived algebraic geometry, with several applications to moduli theory. In brief, the objects of the category $\mathcal{F}_{c}(X)$ are Legendrian morphisms; the morphism spaces and composition operations are defined using equivariant descent. We also establish that $\mathcal{F}_{c}(X)$ embeds into an $(\infty, 2)$-category of spans defined by the AKSZ construction. We further evaluate topological cobordisms as Lagrangian correspondences to define derived Legendrian surgery. |
| title | A Derived Legendrian Category for Shifted Contact Stacks |
| topic | Algebraic Geometry Symplectic Geometry 14A20, 14A30, 14F08 |
| url | https://arxiv.org/abs/2605.13792 |