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Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces
- Source :
- Bulletin de la société mathématique de France, Bulletin de la société mathématique de France, Société Mathématique de France, A paraître
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- International audience; In my paper at Inventiones 2009, we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle Ψ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf cohomology of both Harris-Taylor perverse sheaves and those of Ψ. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.; Dans [2], on détermine les groupes de cohomologie des espaces de Lubin-Tate par voie globale en calculant les fibres des faisceaux de cohomologie du faisceau pervers des cyclesévanescentscyclesévanescents Ψ d'une variété de Shimura de type Kottwitz-Harris-Taylor. L'ingrédient le plus complexe consistè a contrôler lesfì eches de deux suites spectrales calculant l'une les faisceaux de cohomologie des faisceaux pervers d'Harris-Taylor, et l'autre ceux de Ψ. Dans cet article, nous contournons ces difficultés en utilisant la théorie classique des représentations du groupe mirabolique ainsi qu'un argument géométrique simple. Abstract (Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces) In [2], we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle Ψ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf coho-mology of both Harris-Taylor perverse sheaves and those of Ψ. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.
- Subjects :
- Sheaf cohomology
Shimura variety
Pure mathematics
General Mathematics
Mathematics::Number Theory
Lubin-Tate Spaces
01 natural sciences
Mathematics::Algebraic Topology
Perverse sheaf
Mathematics::Algebraic Geometry
Local system
Mathematics::K-Theory and Homology
0103 physical sciences
perverse sheaf
0101 mathematics
Mathematics::Representation Theory
Mathematics
010102 general mathematics
Cohomology
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Algebra
Spectral sequence
Vanishing cycle
vanishing cycle
Sheaf
Langlands correspondance
010307 mathematical physics
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Subjects
Details
- Language :
- French
- ISSN :
- 00379484 and 1777568X
- Database :
- OpenAIRE
- Journal :
- Bulletin de la société mathématique de France, Bulletin de la société mathématique de France, Société Mathématique de France, A paraître
- Accession number :
- edsair.doi.dedup.....a984d245d49e9a78265527bc53ec37f9