Skip navigation
Please use this identifier to cite or link to this item:
Title: An Elliptic Curve Based Perspective on the Arithmetic of Pell Conics
Authors: Zhao, Roy
Advisors: Skinner, Christopher M.
Contributors: Wang, Xiaoheng
Department: Mathematics
Class Year: 2017
Abstract: Franz Lemmermeyer's previous work laid the framework for a description of the arithmetic of Pell conics, which is analogous to that of elliptic curves. He describes a group law on conics and conjectures the existence of an analogous Tate--Shafarevich group with order the squared ideals of the narrow class group. In this thesis, we provide a cohomological definition of the Tate--Shafarevich group and show that its order is as Lemmermeyer conjectured. Furthermore, we extend Lemmermeyer's work by giving a geometric description of the analogous Tamagawa numbers and compute their values. We also develop a Neron differential for the Pell conic and use it to compute the volume of the curve.
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2020

Files in This Item:
File SizeFormat 
thesis.pdf708.11 kBAdobe PDF    Request a copy

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.