Integral points on symmetric varieties and Satake compatifications

Details Integral points on symmetric varieties and Satake compatifications Integral points on symmetric varieties and Satake compatifications

2006-10-16

arxiv.org/abs/math/0610497v2

Mathematics

Number Theory

to appear in Amer. J. Math

Scientific paper

Let V be an affine symmetric variety defined over 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 symmetic varieties and compute the asymptotic of the volumes of norm balls.

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