Shifted cotangent stacks are shifted symplectic
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 67-90.

On démontre que les champs cotangents décalés sont canoniquement munis d’une structure symplectique décalée. On démontre également que les champs conormaux décalés sont munis d’une structure Lagrangienne canonique. Ces résultats étaient attendus mais aucune démonstration n’était disponible dans le cas des champs d’Artin.

We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true, but no written proof was available in the Artin case.

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DOI : 10.5802/afst.1593
Calaque, Damien 1

1 IMAG, Univ Montpellier, CNRS, Institut Universitaire de France, Montpellier, France
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Calaque, Damien. Shifted cotangent stacks are shifted symplectic. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 67-90. doi : 10.5802/afst.1593. http://archive.numdam.org/articles/10.5802/afst.1593/

[1] Calaque, Damien Three lectures on derived symplectic geometry and topological field theories, Poisson 2012: Poisson Geometry in Mathematics and Physics (Indagationes Mathematicæ), Volume 25, Elsevier, 2014, pp. 926-947 | MR | Zbl

[2] Calaque, Damien Lagrangian structures on mapping stacks and semi-classical TFTs, Stacks and Categories in Geometry, Topology, and Algebra (Pantev, Tony, ed.) (Contemporary Mathematics), Volume 643, American Mathematical Society, 2015 | DOI | MR | Zbl

[3] Calaque, Damien; Pantev, Tony; Toën, Bertrand; Vaquié, Michel; Vezzosi, Gabriele Shifted Poisson Structures and Deformation Quantization, J. Topol., Volume 10 (2017) no. 2, pp. 483-584 | DOI | MR | Zbl

[4] Gaitsgory, Dennis; Rozenblyum, Nick A study in derived algebraic geometry. Vol. II. Deformations, Lie theory and formal geometry, Mathematical Surveys and Monographs, 221, American Mathematical Society, Providence, RI, 2017 no. 2 | MR | Zbl

[5] Haugseng, Rune Iterated spans and classical topological field theories, Math. Z., Volume 289 (2018) no. 3-4, pp. 1427-1488 | DOI | MR | Zbl

[6] Melani, Valerio; Safronov, Pavel Derived coisotropic structures II: stacks and quantization, Selecta Math. (N.S.), Volume 24 (2018) no. 4, pp. 3119-3173 | DOI | MR | Zbl

[7] Pantev, Tony; Toën, Bertrand; Vaquié, Michel; Vezzosi, Gabriele Shifted Symplectic Structures, Publications mathématiques de l’IHÉS, Volume 117 (2013) no. 1, pp. 271-328 | DOI | MR | Zbl

[8] Pridham, J. P. Shifted Poisson and symplectic structures on derived N-stacks, J. Topol., Volume 10 (2017) no. 1, pp. 178-210 | DOI | MR | Zbl

[9] Safronov, P. Quasi-Hamiltonian reduction via classical Chern–Simons theory, Adv. Math., Volume 287 (2016), pp. 733-773 | DOI | MR | Zbl

[10] Toën, Bertrand Champs affines, Sel. Math., New Ser., Volume 12 (2006) no. 1, pp. 39-135 | DOI | MR | Zbl

[11] Toën, Bertrand; Vezzosi, Gabriele Homotopical algebraic geometry. II. Geometric stacks and applications, Mem. Amer. Math. Soc., Volume 193 (2008) no. 902, 224 pages | MR | Zbl

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