Adapted deformations and the Ekedahl-Oort stratifications of Shimura varieties

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Adapted deformations and the Ekedahl-Oort stratifications of Shimura varieties

Type: Doctoral Thesis
Title: Adapted deformations and the Ekedahl-Oort stratifications of Shimura varieties
Author: Yan, Q.
Issue Date: 2017-10-18
Keywords: P-divisible groups
Shimura varieties
Ekedahl-Oort stratifications
Loop groups
Abstract: This thesis concerns the relation bettween the good reduction of Shimura varieties and the associated loop groups. To be precise, by studying the Breuil-Kisin modules of p-divisible groups, we construct a direct morphism from the special fibre of a Shimura varieties of Hodge type to an fpqc subquotient of the associated loop group, and show that the geometric fibres of the morphism gives back the Ekedahl-Oort strata of the Shimura varieties in question. This can be seen as an alternative definition of the Ekedahl-Oort stratification of Shimura varieties, which gives a conceptual explanation of E. Viehmann's new invariants of "truncation of level 1" of loop groups.
Promotor: Supervisors: Bart de Smit; Fabrizio Andreatta
Faculty: Science
University: Leiden
Handle: http://hdl.handle.net/1887/56255
 

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application/pdf Chapter 1 Introduction 333.9Kb View/Open
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application/pdf Summary 261.7Kb View/Open
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application/pdf Acknowledgements_Curriculum Vitae 94.32Kb View/Open
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