Counting rational points on algebraic varieties

T. D. Browning, D. R. Heath-Brown, P. Salberger

Published 2004-10-05, updated 2005-04-22Version 4

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and fixed dimension, and are essentially best possible for varieties of degree at least six.