On the Fine Selmer Group

2017/08/22 by Ahmed Matar, Matar, Ahmed
Arts and Humanities · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1708.06588

openalex publication_date 2017/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E/ℚ be an elliptic curve, p an odd prime and K_∞/K the anticyclotomic ℤ_p-extension of a quadratic imaginary field K. In a previous article the author conjectured that the fine p^∞-Selmer group R_p^∞(E/K_∞) is confinitely generated over ℤ_p. In this note we prove this conjecture assuming some hypotheses on E and p.

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