Resumen de Elliptic curves and special values of L-series

Massimo Bertolini

• Let $E/\mathbb{Q}$ be an elliptic curve, and let $L(E/\mathbb{Q}, s)$ be its Hasse-Weil $L$-series. In this paper, working under certain simplifying assumptions, we sketch a proof of the following result: $L(E/\mathbb{Q}, 1)\not= 0 \Longrightarrow E(\mathbb{Q})$ finite.