Visualizing elements of order four in the Shafarevich-Tate group of an\n elliptic curve

2011/02/15 by Mohammad Sadek, Sadek, Mohammad
Mathematics · #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.1102.2980

openalex publication_date 2011/02/15 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28

Abstract

Let E be an elliptic curve defined over a number field K. Let h be an element\nof order 4 in the Shafarevich-Tate group of E. We prove that h is visible in\ninfinitely many abelian surfaces up to isomorphism. This is to say that there\nare infinitely many abelian surfaces J such that E hookrightarrow J and h lies\nin the kernel of the natural map H¹(K,E)\→ H¹(K,J).\n

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