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.
Accepté le :
Publié le :
DOI : 10.5802/afst.1593
Damien Calaque 1

@article{AFST_2019_6_28_1_67_0, author = {Damien Calaque}, title = {Shifted cotangent stacks are shifted symplectic}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {67--90}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 28}, number = {1}, year = {2019}, doi = {10.5802/afst.1593}, zbl = {1444.14004}, mrnumber = {3940792}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1593/} }
TY - JOUR AU - Damien Calaque TI - Shifted cotangent stacks are shifted symplectic JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 67 EP - 90 VL - 28 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1593/ DO - 10.5802/afst.1593 LA - en ID - AFST_2019_6_28_1_67_0 ER -
%0 Journal Article %A Damien Calaque %T Shifted cotangent stacks are shifted symplectic %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 67-90 %V 28 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1593/ %R 10.5802/afst.1593 %G en %F AFST_2019_6_28_1_67_0
Damien Calaque. 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. https://afst.centre-mersenne.org/articles/10.5802/afst.1593/
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