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Title: Explicit Serre weights for two-dimensional Galois representations
Author: Steinmetz, Misja Frederik Alban
ISNI:       0000 0004 8505 5106
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2020
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Let F be a totally real field and p a prime number. Given a Galois representation ρ : GF → GL2(Fp), we have precise conjectures (see BLGG13) in terms of non-explicit p-adic Hodge theory giving the sets of weights of Hilbert modular forms such that the reduction of the associated Galois representation is isomorphic to ρ. Under the assumption that p is unramified in F an alternative explicit formulation of these sets of weights was proposed in the paper DDR16 replacing the p-adic Hodge theory by local class field theory. Subsequently, the equivalence of the reformulated conjecture to the original conjecture was proved in CEGM17. In this thesis we generalise the conjecture of DDR16 and the proof of equivalence of the two conjectures of CEGM17 to hold for any totally real field F. Thereby, we give an equivalent explicit version of the conjectures on the modularity of two-dimensional Galois representations over totally real fields.
Supervisor: Diamond, Fred Irvin ; Buzzard, Kevin Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available