The stack of microlocal perverse sheaves

Ingo Waschkies

Bulletin de la Société Mathématique de France (2004)

  • Volume: 132, Issue: 3, page 397-462
  • ISSN: 0037-9484

Abstract

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In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.

How to cite

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Waschkies, Ingo. "The stack of microlocal perverse sheaves." Bulletin de la Société Mathématique de France 132.3 (2004): 397-462. <http://eudml.org/doc/272464>.

@article{Waschkies2004,
abstract = {In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.},
author = {Waschkies, Ingo},
journal = {Bulletin de la Société Mathématique de France},
keywords = {sheaf; constructible sheaf; perverse sheaf; microlocal sheaf theory; ind-sheaf; $2$-limit; stack},
language = {eng},
number = {3},
pages = {397-462},
publisher = {Société mathématique de France},
title = {The stack of microlocal perverse sheaves},
url = {http://eudml.org/doc/272464},
volume = {132},
year = {2004},
}

TY - JOUR
AU - Waschkies, Ingo
TI - The stack of microlocal perverse sheaves
JO - Bulletin de la Société Mathématique de France
PY - 2004
PB - Société mathématique de France
VL - 132
IS - 3
SP - 397
EP - 462
AB - In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.
LA - eng
KW - sheaf; constructible sheaf; perverse sheaf; microlocal sheaf theory; ind-sheaf; $2$-limit; stack
UR - http://eudml.org/doc/272464
ER -

References

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  9. [9] —, « Ind-Microlocalization », written by F.Ivorra and I.Waschkies following a manuscript of M.Kashiwara, to appear in Progress in Math., Birkhäuser. 
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  12. [12] —, Ind-sheaves, Astérisque, vol. 271, Société Mathématique de France, Paris, 2001. Zbl0993.32009
  13. [13] S. MacLane – Categories for the working mathematician, 2nd éd., Springer, 1998. Zbl0705.18001MR1712872
  14. [14] M. Sato, T. Kawai & M. Kashiwara – « Hyperfunctions and pseudo-differential equations », Proceedings Katata 1971 (H. Komatsu, éd.), Lecture Notes in Math., vol. 287, Springer, 1973, p. 265–529. Zbl0277.46039MR420735
  15. [15] R. Street – « Categorical structures », Handbook of algebra, vol. 1, North-Holland, 1996, p. 529–577. Zbl0854.18001MR1421811
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