Anne Cortella and Boris Kunyavskii:
On a conjecture of Le Bruyn

cortella@math.univ-fcomte.fr, kunyav@macs.biu.ac.il

Submission: 1998, Aug. 26

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 $N\colon R_{F/k}(\Bbb G_{\ text{m}})\to\Bbb G_{\text{m}}$, is not rational over $k$.

1991 Mathematics Subject Classification: 20G05

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