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Title: Modularity of abelian surfaces over imaginary quadratic fields
Author: Schembri, Ciaran
ISNI:       0000 0004 8506 2947
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2019
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Modular forms for GL(2) over an imaginary quadratic field K are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over K or an associated abelian surface with quaternionic multiplication over K. We give explicit evidence in the way of examples to support this conjecture in the latter case. Furthermore, the quaternionic surfaces given correspond to genuine Bianchi newforms, which answers a question posed by J. Cremona as to whether this phenomenon can happen.
Supervisor: Sengun, Haluk Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available