Geometric retract rationality of norm varieties

TL;DR

This paper proves that norm varieties associated with a prime and invertible elements over a characteristic zero field are geometrically retract rational, extending previous results on their geometric properties.

Contribution

It establishes the geometric retract rationality of norm varieties, generalizing earlier results on their geometric connectedness properties.

Findings

Norm varieties are geometrically retract rational.

Generalization of previous geometric connectedness results.

Extends understanding of norm varieties in algebraic geometry.

Abstract

Let k be a field of characteristic zero. We show that the norm variety associated to a prime $\ell$ and an ordered sequence of invertible elements of k is geometrically retract rational. This generalizes a recent result of Balwe-Hogadi-Sawant, where geometric $\mathbb A^1$-connectedness (an a priori weaker notion) had been proven.