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Abstract
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We consider the Noether Problem for stable and retract rationality for the sequence of
-torsion
subgroups
of a torus
,
.
We show that the answer to these questions only depends on
, where
is the period of
the generic
-torsor.
When
is the norm one torus associated to a finite Galois extension, we find all
such
that the Noether Problem for retract rationality has a positive solution for
. We
also give an application to the Grothendieck ring of stacks.
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Keywords
Noether problem, algebraic tori, retract rationality
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Mathematical Subject Classification 2010
Primary: 14L15, 14M20
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Milestones
Received: 1 May 2019
Revised: 25 December 2019
Accepted: 2 January 2020
Published: 13 July 2020
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