Torsion and twists of abelian varieties

2023/10/17 by Melistas, Mentzelos
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.11086

Abstract

In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes over any quadratic extension where odd-order torsion growth is achieved. In particular, we show that for every rational elliptic curve and every imaginary quadratic field not equal to ℚ(√(-3)) satisfying the Heegner hypothesis no odd-order torsion growth can occur.

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