UBC Number Theory Seminar: Sujatha Ramdorai

Let 𝐸 be an elliptic curve over an imaginary quadratic number field 𝐾 and let 𝑝 be an odd prime number. Greenberg introduced a topology for the family of linearly independent ℤ𝑝 extensions of 𝐹 for any number field 𝐹. A conjecture of Mazur predicts that the growth of rational points of 𝐸 along a ℤ𝑝 extension of 𝐾 is bounded unless the extension is the anticyclotomic extension, and the root number of 𝐸 over K is −1. We study the growth of rational points of 𝐸 in the family of ℤ𝑝 extensions and its implications for Mazur's conjecture.