Date of Completion
torsion, elliptic curve, algebraic number theory, function fields, arithmetic geometry, genus
Field of Study
Doctor of Philosophy
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 ≠ 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.
McDonald, Robert John Sweet, "Torsion Subgroups of Elliptic Curves over Function Fields" (2019). Doctoral Dissertations. 2106.