Large Shafarevich-Tate groups over quadratic number fields

2018/01/31 by Myungjun Yu, Yu, Myungjun
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.1801.10536

openalex publication_date 2018/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension over Q. Let ST(E/K) dente the Shafarevich-Tate group of E over K. We show that (under mild conditions on E) for every r>0, there are infinitely many quadratic twists E^d/Q of E/Q such that dim_F2(ST(E^d/K)[2]) > r

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