Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.40282

Authors: Lin, Zichao, Yin, Mulun

Institutions: Chinese Academy of Sciences, University of Massachusetts Amherst, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7215065737

Cites:

Cited by: 1

Related to: 10