A Conjecture of Mazur predicting the growth of Mordell--Weil ranks in Z_p-extensions

Speaker: Debanjana Kundu

Date: Thu, Feb 8, 2024

Location: PIMS, University of British Columbia, Online, Zoom

Conference: UBC Number Theory Seminar

Subject: Mathematics, Number Theory

Class: Scientific


Let \(p\) be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve \(E/\mathbb{Q}\) over an imaginary quadratic field in which \(p\) splits and \(E\) has good reduction at \(p\). In particular, we obtain criteria that may be checked through explicit calculation, thus allowing for the verification of Mazur's conjecture in specific examples. This is joint work with Rylan Gajek-Leonard, Jeffrey Hatley, and Antonio Lei.