2004/04/06 by Laurent Clozel, L. Clozel, Clozel, L. +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Neuroscience · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Neurological Disease Mechanisms and Treatments #Number Theory (math.NT) #Phytochemical Studies and Bioactivities #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0404131
Latex, French, 20. pages, no figure. to appear in Annals of Math
arxiv created 2004/04/06 · openalex publication_date 2004/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 μn is a sequence of such probability measures associated to strongly special subvarieties Zn of S there exists a subsequence μnk which converge to a measure μZ canonically associated to a strongly special subvariety Z and for all k>>0 Znk 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.