Séminaire de Théorie des Nombres de Montpellier :

Le 25 octobre 2004 à None -

Présentée par Browning Tim - Oxford

« Counting rational points on algebraic varieties »

Given a number field $k$ and a projective algebraic variety $V$, an age-old goal in number theory is to relate properties of the set $V(k)$ of $k$-rational points on $V$ to the intrinsic geometry of $V$. Whenever $V(k)$ is Zariski dense in $V$, one intriguing aspect of this problem is revealed by trying to estimate the cardinality of points in $V(k)$ that have height at most $B$, for given $B>1$. The purpose of this talk is to discuss a rather crude conjecture in the field, together with recent progress that has been made upon it.