Integral points on symmetric varieties and Satake compatifications

• Autores: Alexander Gorodnik, Hee Oh, Nimish Shah
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 131, Nº 1, 2009, págs. 1-58
• Idioma: inglés
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• Resumen

  • 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