Work

On Conjectures of $μ$-Invariant for Selmer Groups at $p=2$

Year: 2026

Type: preprint

Abstract: Let $E$ be an elliptic curve define over $\mathbb{Q}$. Further assume $E$ has good ordinary reduction at $p=2$. In this article, we prove Greenberg's conjecture on the value of the algebraic Iwasawa $μ$-invariant when $E$ has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of the $2$-adic $μ$-invariants for all such curves. We also prove the vanishing of the algebraic $μ$-invariant of the fine Selmer group introduced by Coates and Sujatha at $p=2$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31527

Authors: Lin, Zichao, Yin, Mulun

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

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214596686

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