Studying the growth of Mordell-Weil

  • Barry Mazur

  • Karl Rubin


We study the growth of the Mordell-Weil groups of an elliptic curve as runs through the intermediate fields of a -extension. We describe those -extensions 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.