Abstract
Let X be the wonderful compactification of a connected adjoint semisimple
group G defined over a number field. We prove Manin’s conjecture on the asymptotic
(as T ! 1) of the number of K-rational points of X of height less than
T, and give an explicit construction of a measure on X(A), generalizing Peyre’s
measure, which describes the asymptotic distribution of the rational points G(K)
on X(A). Our approach is based on the mixing property of L2(G(K)\G(A)) which
we obtain with a rate of convergence.
group G defined over a number field. We prove Manin’s conjecture on the asymptotic
(as T ! 1) of the number of K-rational points of X of height less than
T, and give an explicit construction of a measure on X(A), generalizing Peyre’s
measure, which describes the asymptotic distribution of the rational points G(K)
on X(A). Our approach is based on the mixing property of L2(G(K)\G(A)) which
we obtain with a rate of convergence.
| Translated title of the contribution | Manin's and Peyre's conjectures on rational points and adelic mixing |
|---|---|
| Original language | English |
| Pages (from-to) | 385-437 |
| Number of pages | 51 |
| Journal | Annales Scientifiques de l'École Normale Supérieure |
| Volume | 41 |
| Issue number | 3 |
| Publication status | Published - May 2008 |