On the $2$-Selmer group of Jacobians of hyperelliptic curves

Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría

Let $\mathcal{C}$ be a hyperelliptic curve $y^2=p(x)$ defined over a number field $K$ with $p(x)$ integral of odd degree. The purpose of the present article is to prove lower and…