Residual Supersingular Iwasawa Theory over quadratic imaginary fields

2022/06/08 by Parham Hamidi, Hamidi, Parham · 1 citation
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2206.03679

openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime and let E be an elliptic curve defined over a quadratic imaginary field where p splits completely. Suppose E has supersingular reduction at primes above p. We define and study the fine double-signed residual Selmer groups in these settings for Z_p²-extensions. We prove that for two residually isomorphic elliptic curves, the vanishing of the signed μ-invariants of one elliptic curve implies the vanishing of the signed μ-invariants of the other. Finally, we show that the Pontryagin dual of the Selmer group and the double-signed Selmer groups have no non-trivial pseudo-null submodules for these extensions.

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