A bound on the μ-invariants of supersingular elliptic curves

2024/09/26 by Rylan Gajek-Leonard, Gajek-Leonard, Rylan · 1 citation
Computer Science · Engineering · Mathematics · #11R23 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.18021

openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E/ℚ be an elliptic curve and let p be a prime of good supersingular reduction. Attached to E are pairs of Iwasawa invariants μ_p^± and λ_p^± which encode arithmetic properties of E along the cyclotomic ℤ_p-extension of ℚ. A well-known conjecture of B. Perrin-Riou and R. Pollack asserts that μ_p^±=0. We provide support for this conjecture by proving that for any ℓ≥ 0, we have μ_p^±≤ 1 for all but finitely many primes p with λ_p^±=ℓ. Assuming a recent conjecture of D. Kundu and A. Ray, our result implies that μ_p^±≤ 1 holds on a density 1 set of good supersingular primes for E.

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• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

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