On a conjecture of Le Bruyn

Anne Cortella; Boris Kunyavskii

On a conjecture of Le Bruyn

Algebraic Geometry 2007-05-23 v1

Authors: Anne Cortella , Boris Kunyavskii

Abstract

Given a generic field extension F/k of degree n>3 (i.e. the Galois group of the normal closure of F is isomorphic to the symmetric group $S_n$ ), we prove that the norm torus, defined as the kernel of the norm map $N:R_{F/k}(G_m)\to\G_m$ , is not rational over k.

Keywords

algebraic tori galois theory

Cite

@article{arxiv.math/9803103,
  title  = {On a conjecture of Le Bruyn},
  author = {Anne Cortella and Boris Kunyavskii},
  journal= {arXiv preprint arXiv:math/9803103},
  year   = {2007}
}

Comments

4 pages, AMSTeX

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