Minseok Kim

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math.NT2025

$p$ -twisted Selmer near-companion curves

Minseok Kim

Let $E_{1}$ and $E_{2}$ be elliptic curves over a number field $K$ . In \cite{scc}, Mazur and Rubin define the concept of $n$ -Selmer near-companions and conjecture that if $E_{1}$ and $E_…

math.NT2025

Increasing the p-Selmer rank by twisting

Minseok Kim

In this paper, we study the $p$ -Selmer groups in the family of $p$ -twists of an elliptic curve $E$ over a number field $K$ . We prove that if $E / K$ is an elliptic curve over a numbe…

p-twisted Selmer near-companion curves

Increasing the p-Selmer rank by twisting

$p$ -twisted Selmer near-companion curves