Abstract

We consider an elliptic curve E which does not admit complex multiplication, and discuss its arithmetic over the cyclotomic Z_p-extension and more general p-adic Lie extensions of various base fields F. After reviewing some known results over number fields, we shift our focus to the case of global function fields. In this context, we introduce an invariant which is defined without assuming the finiteness of the Selmer group of E over the base field F.

About Yukako Kezuka

She works in the field of algebraic number theory. Her mathematical interests include the Birch-Swinnerton-Dyer conjecture, Iwasawa theory, class numbers, Euler systems and the Tamagawa Number Conjecture of Bloch and Kato.

https://webusers.imj-prg.fr/~yukako.kezuka/research.html