Reduction theorems for Noether's problem
Authors:
Mingchang Kang and Bernat Plans
Journal:
Proc. Amer. Math. Soc. 137 (2009), 18671874
MSC (2000):
Primary 12F12, 12F20, 13A50, 11R32, 14E08
Published electronically:
January 6, 2009
MathSciNet review:
2480265
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Abstract: Let be any field, and be a finite group. Let act on the rational function field by automorphisms and . Denote by the fixed field. Noether's problem asks whether is rational (= purely transcendental) over . We will give several reduction theorems for solving Noether's problem. For example, let be a direct product of finite groups. Theorem. Assume that is rational over . Then is rational over . In particular, if is rational (resp. retract rational) over , so is over .
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Additional Information
Mingchang Kang
Affiliation:
Department of Mathematics and Taida Institute of Mathematical Sciences, National Taiwan University, Taipei, Taiwan
Email:
kang@math.ntu.edu.tw
Bernat Plans
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Spain
Email:
bernat.plans@upc.edu
DOI:
http://dx.doi.org/10.1090/S0002993909096087
PII:
S 00029939(09)096087
Keywords:
Noether's problem,
rationality problem,
retract rational.
Received by editor(s):
August 29, 2007
Received by editor(s) in revised form:
March 7, 2008
Published electronically:
January 6, 2009
Additional Notes:
The secondnamed author was partially supported by MTM200604895 (Ministerio de Educación y Ciencia) and by 2005SGR00557 (Generalitat de Catalunya).
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2009
American Mathematical Society
