%0 Journal Article
%T On the rank of the fibres of rational elliptic surfaces
%A Cecilia Salgado
%J Mathematics
%D 2013
%I arXiv
%X We consider an elliptic surface $\pi: \mathcal{E}\rightarrow \mathbb{P}^1$ defined over a number field $k$ and study the problem of comparing the rank of the special fibres over $k$ with that of the generic fibre over $k(\mathbb{P}^1)$. We prove, for a large class of rational elliptic surfaces, the existence of infinitely many fibres with rank at least equal to the generic rank plus two.
%U http://arxiv.org/abs/1307.5912v1