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Peer-reviewedCC BY 4.0Comptes Rendus. Mathématique

The γ-support as a micro-support

  • Tomohiro Asano
  • Stéphane Guillermou
  • Vincent Humilière
  • Yuichi Ike
  • Claude Viterbo
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Abstract

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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Cite

BibTeXRIS
BibTeX
@article{asano2026γsupport,
  title = {{The $\gamma$-support as a micro-support}},
  author = {Tomohiro Asano and Stéphane Guillermou and Vincent Humilière and Yuichi Ike and Claude Viterbo},
  journal = {Comptes Rendus. Mathématique},
  year = {2026},
  month = oct,
  doi = {10.5802/crmath.499},
  eprint = {2211.13945},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-03952989v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - The γ-support as a micro-support
AU  - Tomohiro Asano
AU  - Stéphane Guillermou
AU  - Vincent Humilière
AU  - Yuichi Ike
AU  - Claude Viterbo
PY  - 2026
DA  - 2026/10/16
JO  - Comptes Rendus. Mathématique
DO  - 10.5802/crmath.499
UR  - https://hal.science/hal-03952989v2
AB  - 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.
SN  - 1631-073X
SN  - 1778-3569
ER  -