发表机构
University of Massachusetts Amherst; Morningside Center of Mathematics; Academy of Mathematics and Systems Sciences, Chinese Academy of Science（马萨诸塞大学阿默斯特分校; 中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了有理椭圆曲线在Eisenstein素数处关于Selmer群代数Iwasawa μ-不变量的Greenberg猜想，并通过Iwasawa主猜想确认了Stevens关于解析μ-不变量的猜想。
AI 中文摘要
设$E/\mathbb{Q}$为椭圆曲线，$p$为$E$的奇普通约化素数，并假设$E$具有有理$p$-同源。本文证明了Greenberg猜想，即关于$E$在有理数的分圆$\mathbb{Z}_p$-扩张上的Selmer群的代数Iwasawa $\mu$-不变量消失的猜想。通过椭圆曲线在Eisenstein素数处的Iwasawa主猜想，我们也证实了Stevens关于解析$\mu$-不变量行为的猜想。
英文摘要
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.
Comments20 pages. Comments welcome!
