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arXiv · 1102.2980

Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve

Mohammad Sadek
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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).

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Mohammad Sadek. 2011-02-15. Visualizing elements of order four in the Shafarevich-Tate group of an elliptic curve. https://arxiv.org/abs/1102.2980

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