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Title: The arithmetic of p-adic Hilbert modular forms
Author: Sasaki, Shu
ISNI:       0000 0001 3553 4393
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2008
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The underlying motivation of the thesis is to generalise the techniques of Buzzard-Taylor and Buzzard to a totally real field F. Their novel approach to modularity of Galois representations via knowing conditions under which an overconvergent Up-eigenform is indeed a classical modular forms, was instrumental in proving new cases of Arlin conjecture for Q and has also been important in the modern theory of p-adic modular forms. My thesis is an exploration of their ideas in the Hilbert case. Analytic continuation of overconvergent Hilbert eigenfor~s depends fundamentally on the rigid geometry of Hilbert modular varieties. The model Deligne-Pappas considered, is highly singular at fibres over ramified primes and in order to avoid technical problems arising from geometry, I construct, in the first chapter, a model over the integers of a finite extension of Qp which desingularises the Deligne-Pappas model, using ideas from Pappas-Rapoport on local models. In the second chapter, I prove an analogue. in the Hilbert case where p splits completely in F, of Coleman's theorem- an overconvergent Up-eigenform of small slope is classical. The methodology is to generalise the earlier work of Buzzard on analytic continuation of overconvergent Up-eigenforms (non-ordinary loci) and then apply Kassaei's idea (ordinary loci) to glue overconvergent forms in the absence of companion forms.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available