Date of Completion

4-18-2019

Embargo Period

4-18-2019

Keywords

torsion, elliptic curve, algebraic number theory, function fields, arithmetic geometry, genus

Major Advisor

Álvaro Lozano-Robledo

Associate Advisor

Keith Conrad

Associate Advisor

Liang Xiao

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

Let 𝔽 be a finite field of characteristic p, and C/𝔽 be a smooth, projective, absolutely irreducible curve. Let 𝔽(C) be the function field of C. When the genus of C is 0, and p β‰  2, 3, Cox and Parry provide a minimal list of prime-to-p torsion subgroups that can appear for an elliptic curve E/K. In this thesis, we extend this result by determining the complete list of full torsion subgroups possible for an elliptic curve E/K for any prime p when the genus of C is 0 or 1.

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