The anticyclotomic main conjectures for elliptic curves

TL;DR

This paper proves the main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, covering both ordinary and supersingular primes under mild assumptions.

Contribution

It provides a proof of the Iwasawa main conjectures for elliptic curves in the anticyclotomic setting, extending previous results to more general cases.

Findings

Proof of Iwasawa main conjectures for elliptic curves over anticyclotomic extensions

Valid for both ordinary and supersingular primes

Operates under mild arithmetic assumptions

Abstract

The goal of this article is to obtain a proof of the Main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, under mild arithmetic assumptions, both in the case where the rational prime $p$ is good ordinary or supersingular.