A geometric perspective on Amitsur's conjecture

TL;DR

This paper offers a geometric proof of Roquette's result on Amitsur's conjecture for Severi-Brauer varieties, simplifying the understanding of their birational properties through explicit isomorphisms.

Contribution

It introduces a geometric approach to prove Roquette's theorem, replacing algebraic methods with explicit birational isomorphisms.

Findings

Established a geometric proof for Roquette's result

Provided explicit birational isomorphisms for Severi-Brauer varieties

Simplified the understanding of Amitsur's conjecture in this context

Abstract

Roquette proved Amitsur's conjecture for Severi-Brauer varieties associated with cyclic algebras using algebraic methods. We present a geometric proof of Roquette's result, providing simple and explicit birational isomorphisms.