Studying the growth of Mordell-Weil (Q1419621)
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scientific article; zbMATH DE number 2028845
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Studying the growth of Mordell-Weil |
scientific article; zbMATH DE number 2028845 |
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Studying the growth of Mordell-Weil (English)
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19 January 2004
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Summary: We study the growth of the Mordell-Weil groups \(E(K_n)\) of an elliptic curve \(E\) as \(K_n\) runs through the intermediate fields of a \(\mathbb Z_p\)-extension. We describe those \(\mathbb Z_p\)-extensions \(K_\infty/K\) where we expect the ranks to grow to infinity. In the cases where we know or expect the rank to grow, we discuss where we expect to find the submodule of universal norms.
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