Author

Zi-Chao Lin

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Preprint Sep 2026

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

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 $\mu$-invariant when $E$ has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of the $2$-adic $\mu...

Zi-Chao Lin, Mu-Lun Yin · 0 citations

Preprint Sep 2026

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

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 $\mu$-invariants of the Selmer groups attached to $E$ over the cyclotomic $\mathbb{Z}...

Zi-Chao Lin, Mu-Lun Yin · 2 citations

Preprint Sep 2026

Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-Extensions

Let $E$ be an elliptic curve defined over rational numbers. Further assume $E$ has good ordinary reduction at $p=2$ and $E[4]$ is reducible as a $G_\mathbb{Q}$-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa $\mu$-invariant over the cyclotomic $\mathbb{Z...

Zi-Chao Lin, Mu-Lun Yin · 0 citations