Let $V$ be an affine symmetric variety defined over $\Bbb Q$. We compute the asymptotic distribution of the angular components of the integral points in $V$. This distribution is described by a family of invariant measures concentrated on the Satake boundary of $V$. In the course of the proof, we describe the structure of the Satake compactifications for general affine symmetric varieties and compute the asymptotic of the volumes of norm balls.
|Translated title of the contribution||Integral points on symmetric varieties and Satake compatifications|
|Pages (from-to)||1 - 57|
|Number of pages||57|
|Journal||American Journal of Mathematics|
|Volume||131, issue 1|
|Publication status||Published - Feb 2009|