Vol. 306, No. 2, 2020

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On the Noether Problem for torsion subgroups of tori

Federico Scavia

Vol. 306 (2020), No. 2, 699–719

We consider the Noether Problem for stable and retract rationality for the sequence of d-torsion subgroups T[d] of a torus T, d 1. We show that the answer to these questions only depends on d(mode(T)), where e(T) is the period of the generic T-torsor. When T is the norm one torus associated to a finite Galois extension, we find all d such that the Noether Problem for retract rationality has a positive solution for T[d]. We also give an application to the Grothendieck ring of stacks.

Noether problem, algebraic tori, retract rationality
Mathematical Subject Classification 2010
Primary: 14L15, 14M20
Received: 1 May 2019
Revised: 25 December 2019
Accepted: 2 January 2020
Published: 13 July 2020
Federico Scavia
Department of Mathematics
University of British Columbia
Vancouver BC