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Déterminant microlocal d'un faisceau pervers

Abstract : Following ideas of B. Malgrange, we construct a new invariant for
perverse sheaves: the microlocal determinant. It is a generalization to perverse sheaves of the first secondary characteristic class for flat bundles.

The microlocal determinant is a cohomology class on the cotangent bundle with support in the characteristic variety: it is constructed with the determinants of the local systems obtained from the microlocalizations along the strata.

To show its existence, we put the perverse sheaf in generic position
using canonical transforms and controlling the behavior of the microlocalized through such a transform. We are then reduced
to the dimension 2 case where an explicit computation is performed
using Ph. Maisonobe's combinatorial description of perverse sheaves.
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Contributor : Tristan Torrelli <>
Submitted on : Thursday, December 15, 2005 - 1:54:00 PM
Last modification on : Monday, October 12, 2020 - 10:27:29 AM
Long-term archiving on: : Saturday, April 3, 2010 - 7:17:23 PM


  • HAL Id : tel-00011209, version 1



Raphaël Bondu. Déterminant microlocal d'un faisceau pervers. Mathématiques [math]. Université Nice Sophia Antipolis, 2002. Français. ⟨tel-00011209⟩



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