Number theoretic techniques in the theory of Lie groups and differential geometry

Gopal Prasad; Andrei S. Rapinchuk

Number theoretic techniques in the theory of Lie groups and differential geometry

Differential Geometry 2008-09-16 v1 Number Theory

Authors: Gopal Prasad , Andrei S. Rapinchuk

Abstract

The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense subgroups in a semi-simple Lie group. We have shown that for arithmetic subgroups, weak commensurability has surprisingly strong consequences. Our proofs make use of p-adic techniques and results from algebraic and transcendental number theory.

Keywords

locally symmetric spaces weak commensurability arithmetic subgroups p-adic techniques algebraic number theory transcendental number theory

Cite

@article{arxiv.0809.2401,
  title  = {Number theoretic techniques in the theory of Lie groups and differential geometry},
  author = {Gopal Prasad and Andrei S. Rapinchuk},
  journal= {arXiv preprint arXiv:0809.2401},
  year   = {2008}
}

Comments

This is a slightly revised version of a survey article published in the Proceedings of the International Congress of Chinese Mathematicians held in 2007

Number theoretic techniques in the theory of Lie groups and differential geometry

Abstract

Keywords

Cite

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