The Distribution of Integral Points on the Wonderful Compactification by Height

TL;DR

This paper investigates how S-integral points of bounded height are distributed asymptotically on certain compactifications of semi-simple groups, providing insights into their geometric and arithmetic properties.

Contribution

It introduces a new analysis of the distribution of integral points on partial bi-equivariant compactifications, expanding understanding of height functions in this context.

Findings

Asymptotic formulas for the distribution of integral points.

Identification of key geometric structures influencing distribution.

Extension of height distribution results to new classes of compactifications.

Abstract

We study the asymptotic distribution of S-integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.