Automorphisms of Drinfeld half-spaces over a finite field

TL;DR

This paper proves that the automorphism group of Drinfeld's half-space over a finite field is exactly the projective linear group, using Berkovich analytic geometry and considering base field extensions.

Contribution

It establishes the automorphism group of Drinfeld's half-space over finite fields as the projective linear group, employing Berkovich geometry techniques.

Findings

Automorphism group is the projective linear group

Uses Berkovich analytic geometry over finite fields

Considers extensions of the base field

Abstract

We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with the trivial valuation. We also take into account extensions of the base field.