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Integral points on symmetric varieties and Satake compatifications
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 1, February 2009
- pp. 1-57
- 10.1353/ajm.0.0034
- Article
- Additional Information
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.