×

Studying the growth of Mordell-Weil. (English) Zbl 1142.11339

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.

MSC:

11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11G05 Elliptic curves over global fields
11R23 Iwasawa theory
14G05 Rational points
PDF BibTeX XML Cite
Full Text: EuDML EMIS