English

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

Number Theory 2022-06-14 v3 Algebraic Geometry Dynamical Systems

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.

Keywords

Cite

@article{arxiv.1910.04568,
  title  = {The space of homogeneous probability measures on $\overline{\Gamma\backslash X}^S_{\rm max}$ is compact},
  author = {Christopher Daw and Alexander Gorodnik and Emmanuel Ullmo and Jialun Li},
  journal= {arXiv preprint arXiv:1910.04568},
  year   = {2022}
}

Comments

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