Comptes Rendus
Géométrie et Topologie
The γ-support as a micro-support
Tomohiro Asano1 ; Stéphane Guillermou2 ; Vincent Humilière3  ; Yuichi Ike4 ; Claude Viterbo5
1 Faculty of Electrical, Information and Communication Engineering, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, 920-1192, Japan
2 UMR CNRS 6629 du CNRS Laboratoire de Mathématiques Jean LERAY 2 Chemin de la Houssinière, BP 92208, F-44322 NANTES Cedex 3 France
3 Sorbonne Université and Université de Paris, CNRS, IMJ-PRG, F-75005 Paris, France and Institut Universitaire de France
4 Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
5 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1333-1340.

We prove that for any element L in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the γ-support of L coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of γ-support.

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DOI : 10.5802/crmath.499
Tomohiro Asano 1 ; Stéphane Guillermou 2 ; Vincent Humilière 3 ; Yuichi Ike 4 ; Claude Viterbo 5

1 Faculty of Electrical, Information and Communication Engineering, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, 920-1192, Japan
2 UMR CNRS 6629 du CNRS Laboratoire de Mathématiques Jean LERAY 2 Chemin de la Houssinière, BP 92208, F-44322 NANTES Cedex 3 France
3 Sorbonne Université and Université de Paris, CNRS, IMJ-PRG, F-75005 Paris, France and Institut Universitaire de France
4 Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
5 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {The $\gamma $-support as a micro-support},
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Tomohiro Asano; Stéphane Guillermou; Vincent Humilière; Yuichi Ike; Claude Viterbo. The $\gamma $-support as a micro-support. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1333-1340. doi : 10.5802/crmath.499. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.499/

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