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

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

2011-02-15

arxiv.org/abs/1102.2980v3

Mathematics

Number Theory

This paper has been drawn by the author due to an error in the proof of Theorem 4.1

Scientific paper

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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