On a conjecture of Le Bruyn

Details On a conjecture of Le Bruyn On a conjecture of Le Bruyn

1998-03-23

arxiv.org/abs/math/9803103v1

Mathematics

Algebraic Geometry

4 pages, AMSTeX

Scientific paper

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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