$p$-retract Rationality and Norm One Tori

We study whether the norm one torus associated with a finite separable non-Galois field extension $K/k$ is $p$-retract rational over $k$ for a prime $p$, focusing on the case where the Galois group of the Galois closure of $K/k$ is either the symmetric or the alternating group.

Publication Details

Journal
ArXiv.org
Published
2025-10-11
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

$p$-retract Rationality and Norm One Tori

ArXiv.org
Algebraic Geometry and Number Theory
article

$p$-retract Rationality and Norm One Tori

article en

Abstract

We study whether the norm one torus associated with a finite separable non-Galois field extension $K/k$ is $p$-retract rational over $k$ for a prime $p$, focusing on the case where the Galois group of the Galois closure of $K/k$ is either the symmetric or the alternating group.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 37%
Algebraic Geometry and Number Theory
Open Access PDFOpenAlex
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$p$-retract Rationality and Norm One Tori · ArXiv.org (2025) | TGRS Research Map | TGRS