Varieties with too many rational points
We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.
math.NT↗
arXiv subjects
D. Loughran
Publications and source records attributed to D. Loughran.
Failures of weak approximation in families
Given a family of varieties $X\to \mathbb{P}^n$ over a number field $k$, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for $100\%$ of the fibres which are everywhere locally soluble.
math.NT↗