Buildings, Extensions, and Volume Growth Entropy

TL;DR

This paper explores how volume measures on Bruhat-Tits buildings associated with a split semisimple group over a local field and its extension can be compared, shedding light on geometric properties of these structures.

Contribution

It introduces a method to compare volume measures on Bruhat-Tits buildings over a field and its extension for split semisimple groups.

Findings

Established a comparison framework for volumes on B_E and B_F

Provided insights into geometric properties of buildings over different fields

Enhanced understanding of volume growth in non-Archimedean settings

Abstract

Let F be a non-Archimedean local field and let E be a finite extension of F. Let G be a split semisimple F group. We discuss how to compare volumes on the Bruhat-Tits buildings B_E and B_F of G(E) and G(F) respectively.