Main conjectures for non-CM elliptic curves at good ordinary primes

TL;DR

This paper advances the understanding of Iwasawa main conjectures and BSD formula for non-CM elliptic curves at good ordinary primes, especially for cases with low rank and irreducible residue representations.

Contribution

It proves new cases of Iwasawa main conjectures and extends results on the p-converse theorem and BSD formula for elliptic curves with rank ≤ 1.

Findings

More cases of Iwasawa main conjectures proved

Extended p-converse theorem to broader cases

Confirmed p-part BSD formula for low-rank elliptic curves

Abstract

Let $E/\mathbb{Q}$ be an elliptic curve and $p > 2$ be a prime of good ordinary reduction for $E$. Assume that the residue representation associated with $(E, p)$ is irreducible. In this paper, we prove more cases on several Iwasawa main conjectures for $E$. As applications, we prove more general cases of $p$-converse theorem and $p$-part BSD formula when the rank is less than or equal to $1$.