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arXiv · 2408.07826

The Iwasawa $\mu$-invariants of Elliptic Curves over $\mathbb{Q}$

Adithya Chakravarthy
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Abstract

In this paper, we discuss a longstanding conjecture of Greenberg in the Iwasawa theory of elliptic curves. Greenberg's conjecture states that if $E/\mathbb{Q}$ is an elliptic curve with good ordinary reduction at $p$, and $E[p]$ is irreducible as a Galois module, then the Selmer group of $E$ over the cyclotomic $\mathbb{Z}_p$ extension of $\mathbb{Q}$ has $\mu$-invariant zero. We prove that if $E$ is an elliptic curve over $\mathbb{Q}$, then we have $\mu \leq 1$ for all but finitely many primes $p$ of good ordinary reduction.

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Adithya Chakravarthy. 2024-08-14. The Iwasawa $\mu$-invariants of Elliptic Curves over $\mathbb{Q}$. https://arxiv.org/abs/2408.07826

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