In this thesis, we prove local-global compatibility results at ℓ = p for the torsion automorphic Galois representations constructed by Scholze, generalising the work of Caraiani–Newton. In particular, we verify, up to a nilpotent ideal, the local-global compatibility conjecture at ℓ = p of Gee–Newton in the case of imaginary CM fields under some technical assumptions. The key new ingredient is a local-global compatibility result for Q-ordinary self-dual automorphic representations for arbitrary parabolic subgroups.
| Date of Award | 1 Oct 2024 |
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| Original language | English |
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| Awarding Institution | |
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| Supervisor | Fred Diamond (Supervisor) & Ana Caraiani (Supervisor) |
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Ordinary parts and local-global compatibility at ℓ = p
Hevesi, B. (Author). 1 Oct 2024
Student thesis: Doctoral Thesis › Doctor of Philosophy