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arXiv · 2609.40282

On Greenberg's conjecture for rational elliptic curves at Eisenstein primes

Zichao Lin·Mulun Yin
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Abstract

Let $E/\mathbb{Q}$ be an elliptic curve, and let $p$ be an odd prime of ordinary reduction for $E$, and assume that $E$ admits a rational $p$-isogeny. In this paper we prove Greenberg's conjecture on the vanishing of algebraic Iwasawa $μ$-invariants of the Selmer groups attached to $E$ over the cyclotomic $\mathbb{Z}_p$-extension of the rational numbers. Via the Iwasawa Main Conjecture for elliptic curves at Eisenstein primes, we also confirm Stevens's conjecture on the behavior of analytic $μ$-invariants.

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Zichao Lin, Mulun Yin. 2026-09-30. On Greenberg's conjecture for rational elliptic curves at Eisenstein primes. https://arxiv.org/abs/2609.40282

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