Rational points on cubic hypersurfaces
by
Tim Browning
University of Bristol

Given a cubic hypersurface defined over the rationals, the Hardy-Littlewood method allows one to show that the rational points on it are Zariski dense if the dimension is sufficiently large. Thanks to the work of Davenport, and more recently of Heath-Brown, we can now handle arbitrary hypersurfaces of dimension at least 12. In this talk I show that one extend this to dimension 11, provided that the underlying cubic form can be written as the sum of two forms that have no variables in common.

Date received: April 12, 2008