Integral points on symmetric varieties and Satake compatifications

A Gorodnik; H Oh; N Shah

Integral points on symmetric varieties and Satake compatifications

A Gorodnik
, H Oh
, N Shah

Research output: Contribution to journal › Article (Academic Journal) › peer-review

18 Citations (Scopus)

Abstract

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
Original language	English
Pages (from-to)	1 - 57
Number of pages	57
Journal	American Journal of Mathematics
Volume	131, issue 1
Publication status	Published - Feb 2009

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Publisher: Johns Hopkins University Press

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http://muse.jhu.edu/journals/ajm/summary/v131/131.1.gorodnik.html

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title = "Integral points on symmetric varieties and Satake compatifications",

abstract = "Let \$V\$ be an affine symmetric variety defined over \$\textbackslash{}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.",

author = "A Gorodnik and H Oh and N Shah",

note = "Publisher: Johns Hopkins University Press",

year = "2009",

month = feb,

language = "English",

volume = "131, issue 1",

pages = "1 -- 57",

journal = "American Journal of Mathematics",

issn = "1080-6377",

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TY - JOUR

T1 - Integral points on symmetric varieties and Satake compatifications

AU - Gorodnik, A

AU - Oh, H

AU - Shah, N

N1 - Publisher: Johns Hopkins University Press

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

M3 - Article (Academic Journal)

SN - 1080-6377

VL - 131, issue 1

SP - 1

EP - 57

JO - American Journal of Mathematics

JF - American Journal of Mathematics

ER -

Integral points on symmetric varieties and Satake compatifications

Abstract

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