AuthorAl-Shammari, Fahd M.
AdvisorMcCallum, William G.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractLet K be a number field. By representing genus one curves as plane quintic curves with 5 double points, we construct (up to birational equivalence) the universal elliptic curves defined over the modular curves X₁(5) and X(μ)(5) (X(μ)(5) is the modular curve parameterizing pairs (E, i : (μ)₅ → E) where E is an elliptic curve over Q). We then twist the latter by elements coming from H¹(Gal(K̅/K), (μ)₅) to construct universal families of principal homogeneous spaces for the curves E. Finally we show that every principal homogeneous space arising this way is visible in some abelian variety.
Degree ProgramGraduate College