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Title: On Galois representations associated to low weight Hilbert-Siegel modular forms
Author: Weiss, Ariel
ISNI:       0000 0004 8501 3192
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2019
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Under the Langlands correspondence, where automorphic representations of GLₙ should correspond to n-dimensional Galois representations, 'cuspida' automorphic representations should correspond to 'irreducible' Galois representations. More generally, heuristically, one expects that the image of an automorphic Galois representation should be as large as possible, unless there is an automorphic reason for it to be small. This thesis addresses the consequence of this heuristic for low weight, genus 2 Hilbert-Siegel modular forms. Let F be a totally real field and π=⊗'νπν be a cuspidal automorphic representation of GSp₄(A_F), whose archimedean components lie in the holomorphic (limit of) discrete series. If π is not CAP or endoscopic, then we show that its associated ℓ-adic Galois representation ρπ,ℓ is irreducible and crystalline for 100% of primes. If, moreover, π is neither an automorphic induction nor a symmetric cube lift, then we show that, for 100% of primes ℓ, the image of its mod ℓ Galois representation contains Sp₄(Fℓ).
Supervisor: Berger, Tobias Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available