The supersingular locus of the Shimura variety of GU(1,s)
The supersingular locus of the Shimura variety of GU(1,s)
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DissertationPrüfungsdatum
01.09.2005Datum der Veröffentlichung
2005Erstgutachter
Rapoport, MichaelZweitgutachter
Zink, ThomasMetadaten
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Inhalt
In this paper I study the supersingular locus of the reduction modulo p of the Shimura variety of GU(1,s) in the case of an inert prime p. Using Dieudonné theory I define a stratification of the k-rational points of the corresponding moduli space of p-divisible groups for every algebraically closed field k of characterstic p. I describe the incidence relation of this stratification.
In the case of GU(1,2), I use this results to show that the supersingular locus is purely of dimension 1 and of complete intersection. I give an explicit description of its irreducible components and their intersection behaviour.
In the case of GU(1,2), I use this results to show that the supersingular locus is purely of dimension 1 and of complete intersection. I give an explicit description of its irreducible components and their intersection behaviour.
Schlagwörter
p-divisible Gruppen, Modulräume abelscher Varietäten, Rapoport-Zink-Räume, p-divisible groups, moduli spaces of abelian varieties, Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Algebraic moduli of abelian varieties classification
Klassifikation (DDC)
510 MathematikVollaard, Inken-Kareen: The supersingular locus of the Shimura variety of GU(1,s). - Bonn, 2005. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-05884
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-05884
@phdthesis{handle:20.500.11811/2307,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-05884,
author = {{Inken-Kareen Vollaard}},
title = {The supersingular locus of the Shimura variety of GU(1,s)},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2005,
note = {In this paper I study the supersingular locus of the reduction modulo p of the Shimura variety of GU(1,s) in the case of an inert prime p. Using Dieudonné theory I define a stratification of the k-rational points of the corresponding moduli space of p-divisible groups for every algebraically closed field k of characterstic p. I describe the incidence relation of this stratification.
In the case of GU(1,2), I use this results to show that the supersingular locus is purely of dimension 1 and of complete intersection. I give an explicit description of its irreducible components and their intersection behaviour.},
url = {https://hdl.handle.net/20.500.11811/2307}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-05884,
author = {{Inken-Kareen Vollaard}},
title = {The supersingular locus of the Shimura variety of GU(1,s)},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2005,
note = {In this paper I study the supersingular locus of the reduction modulo p of the Shimura variety of GU(1,s) in the case of an inert prime p. Using Dieudonné theory I define a stratification of the k-rational points of the corresponding moduli space of p-divisible groups for every algebraically closed field k of characterstic p. I describe the incidence relation of this stratification.
In the case of GU(1,2), I use this results to show that the supersingular locus is purely of dimension 1 and of complete intersection. I give an explicit description of its irreducible components and their intersection behaviour.},
url = {https://hdl.handle.net/20.500.11811/2307}
}
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