The space of homogeneous probability measures on ${\overline{\Gamma \backslash X}}_{\max }^S$ is compact

Abstract

In this paper we prove that the space of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space is compact. As an application, we explain some consequences for the distribution of weakly special subvarieties of Shimura varieties.

27 pages; appendix by Jialun Li. arXiv admin note: text overlap with arXiv:1809.10090

References in corpus (1)

• Equidistribution of translates of a homogeneous measure on the Borel--Serre boundary