Equidistribution de sous-varietes speciales (Equisistribution of special subvarieties)
| dc.creator | Clozel, L. | |
| dc.creator | Ullmo, E. | |
| dc.date | 2004-04-06 | |
| dc.date.accessioned | 2026-07-07T05:07:13Z | |
| dc.date.available | 2026-07-07T05:07:13Z | |
| dc.description | A strongly special subvariety of a Shimura variety $S$ is (essentially) a subvariety associated to a semi-simple sub-Shimura datum. We prove that the set of probability measures canonically associated to to strongly special subvarieties is compact. More precisely: If $μ_n$ is a sequence of such probability measures associated to strongly special subvarieties $Z_n$ of $S$ there exists a subsequence $μ_{n_k}$ which converge to a measure $μ_Z$ canonically associated to a strongly special subvariety $Z$ and for all $k>>0$ $Z_{n_k}$ is contained in $Z$. We give some application to the Andre-Oort conjecture: If $X$ is a subvariety of $S$ then there exists at most finitely many maximal (amongs subvarieties of $X$) strongly special subvarieties of $X$ as predicted by the Andre-Oort Conjecture. The proof uses Ratner's theory, some results of Mozes-Shah and Dani-Margulis. | |
| dc.description | Latex, French, 20. pages, no figure. to appear in Annals of Math | |
| dc.identifier | https://arxiv.org/abs/math/0404131 | |
| dc.identifier | http://arxiv.org/abs/math/0404131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70773 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Equidistribution de sous-varietes speciales (Equisistribution of special subvarieties) | |
| dc.type | text |