Serre´s conjectures on the number of rational points of bounded height

P. Salberger, Chalmers University
IAS Room S-101

We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired by the local real and p-adic determinant methods of Bombieri-Pila and Heath-Brown.