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
Abstract

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.

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