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
Γlvaro Lozano-Robledo
Associate Advisor
Keith Conrad
Associate Advisor
Liang Xiao
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
Let π½ be a finite field of characteristic p, and C/π½ be a smooth, projective, absolutely irreducible curve. Let π½(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.
Recommended Citation
McDonald, Robert John Sweet, "Torsion Subgroups of Elliptic Curves over Function Fields" (2019). Doctoral Dissertations. 2106.
https://digitalcommons.lib.uconn.edu/dissertations/2106