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On a conjecture of Le Bruyn

Anne Cortella·Boris Kunyavskii
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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.

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Anne Cortella, Boris Kunyavskii. 1998-03-23. On a conjecture of Le Bruyn. https://arxiv.org/abs/math/9803103

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