Rational points: new dimensions is a research project in arithmetic geometry running from September 2023 till September 2028, which is funded by an NWO Open Competition ENW – XL grant and will be carried out by a consortium based at the Universities of Groningen, Leiden, and Utrecht. We will investigate rational points on surfaces and higher-dimensional varieties.

The project is grouped into three themes:

  • The first theme, from curves to surfaces and beyond, consists of projects which take established techniques from the study of rational points on curves and extend them to the substantially more difficult setting of higher-dimensional varieties.
  • The second theme, from characteristic zero to characteristic p, and back, looks at various settings in which geometry in characteristic p is related to arithmetic.
  • Our third theme is from rational points to Campana points: Campana points are an emerging area of research in Diophantine geometry, linking rational and integral points on varieties.