Involutivity of truncated microsupports

Masaki Kashiwara; Térésa Monteiro Fernandes; Pierre Schapira

Bulletin de la Société Mathématique de France (2003)

  • Volume: 131, Issue: 2, page 259-266
  • ISSN: 0037-9484

Abstract

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Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf F on a real manifold and k ∈ ℤ , if two functions vanish on SS k ( F ) , then so does their Poisson bracket.

How to cite

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Kashiwara, Masaki, Monteiro Fernandes, Térésa, and Schapira, Pierre. "Involutivity of truncated microsupports." Bulletin de la Société Mathématique de France 131.2 (2003): 259-266. <http://eudml.org/doc/272436>.

@article{Kashiwara2003,
abstract = {Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf $F$ on a real manifold and $k\in \mathbb \{Z\}$, if two functions vanish on $\operatorname\{SS\}_k(F)$, then so does their Poisson bracket.},
author = {Kashiwara, Masaki, Monteiro Fernandes, Térésa, Schapira, Pierre},
journal = {Bulletin de la Société Mathématique de France},
keywords = {sheaves; microsupport; involutivity},
language = {eng},
number = {2},
pages = {259-266},
publisher = {Société mathématique de France},
title = {Involutivity of truncated microsupports},
url = {http://eudml.org/doc/272436},
volume = {131},
year = {2003},
}

TY - JOUR
AU - Kashiwara, Masaki
AU - Monteiro Fernandes, Térésa
AU - Schapira, Pierre
TI - Involutivity of truncated microsupports
JO - Bulletin de la Société Mathématique de France
PY - 2003
PB - Société mathématique de France
VL - 131
IS - 2
SP - 259
EP - 266
AB - Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf $F$ on a real manifold and $k\in \mathbb {Z}$, if two functions vanish on $\operatorname{SS}_k(F)$, then so does their Poisson bracket.
LA - eng
KW - sheaves; microsupport; involutivity
UR - http://eudml.org/doc/272436
ER -

References

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  1. [1] J.-M. Bony – « Quasi-analycité et unicité du problème de Cauchy pour les solutions d’équations aux dérivées partielles », Équations aux dérivées partielles et analyse fonctionnelle, Séminaire Goulaouic-Schwartz, École Polytechnique Paris, 1971, Exp. 10. Zbl0238.35017
  2. [2] M. Kashiwara, T. Monteiro Fernandes & P. Schapira – « Truncated microsupport and holomorphic solutions of D -modules », ArXiv math.AG/0203091, Annales Sci. École Normale Sup., to appear. Zbl1044.32003MR2013927
  3. [3] M. Kashiwara & P. Schapira – Sheaves on manifolds, Grundlehren der Math. Wiss., vol. 292, Springer Verlag, 1990. Zbl0709.18001MR1074006

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