Counting rational points on hypersurfaces
(Un exposé de Roger Heath-Brown au séminaire de
théorie des nombres de Chevaleret le 24 mai 2004)
Résumé :
For an irreducible algebraic projective hypersurface of dimension $N$
and degree at least $2$ it may be conjectured that there are
$O(B^{N+\varepsilon})$ rational points of height at most $B$,
for any $\varepsilon>0$.
The talk will look at the evidence for this conjecture, and at progress
towards it.