D. Mocanu

New algebraic points on covers of elliptic curves

For a smooth projective curve $C/\mathbb{Q}$ of genus $\geq 2$ and $L/\mathbb{Q}$ an extension, we write $C(L)_{\text{new}}=\{P\in C(L):\mathbb{Q}(P)=L\}$. Recent work of Khawaja and Siksek conjectures that this set is empty for $100\%$ of degree $n$ number fields $L$, when ordered by absolute discriminant. Moreover, t...