Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve
Number Theory
2011-03-02 v3
Abstract
Let E be an elliptic curve defined over a number field K. Let h be an element of order 4 in the Shafarevich-Tate group of E. We prove that h is visible in infinitely many abelian surfaces up to isomorphism. This is to say that there are infinitely many abelian surfaces J such that E\hookrightarrow J and h lies in the kernel of the natural map H^1(K,E)\rightarrow H^1(K,J).
Keywords
Cite
@article{arxiv.1102.2980,
title = {Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve},
author = {Mohammad Sadek},
journal= {arXiv preprint arXiv:1102.2980},
year = {2011}
}
Comments
This paper has been drawn by the author due to an error in the proof of Theorem 4.1