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

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 $1$.

Final version, to appear in Journal of Algebra