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arXiv · 1712.08251

A Homological Definition for the Tate--Shafarevich Group of a Pell Conic

Roy Zhao
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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 article, we provide a cohomological definition of the Tate--Shafarevich group and show that its order is as Lemmermeyer conjectured.

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Roy Zhao. 2017-12-21. A Homological Definition for the Tate--Shafarevich Group of a Pell Conic. https://arxiv.org/abs/1712.08251

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