On local-global divisibility by p² in elliptic curves

2011/03/25 by Laura Paladino, Paladino, Laura, Gabriele Ranieri +3 · 1 citation
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical and Political Studies #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1103.4963

openalex publication_date 2011/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime lager than 3. Let k be a number field, which does not contain the subfield of ℚ (ζ_p²) of degree p over ℚ. Suppose that E is an elliptic curve defined over k. We prove that the existence of a counterexample to the local-global divisibility by p² in E, assures the existence of a k-rational point of exact order p in E. Using the Merel Theorem, we then shrunk the known set of primes for which there could be a counterexample to the local-global divisibility by p².

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