Tokyo Journal of Mathematics

Toward Noether's Problem for the Fields of Cross-ratios


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In this article, we consider an analogue of Noether's problem for the fields of cross-ratios, and discuss on a rationality problem which connects this with Noether's problem. We show that the affirmative answer of the analogue implies the affirmative answer for Noether's Problem for any permutation group with odd degree. We also obtain some negative results for various permutation groups with even degree.

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Tokyo J. of Math. Volume 39, Number 3 (2017), 901-922.

First available in Project Euclid: 6 April 2017

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Digital Object Identifier

Primary: 11E04: Quadratic forms over general fields
Secondary: 11R32: Galois theory 11R34: Galois cohomology [See also 12Gxx, 19A31] 12F12: Inverse Galois theory 12F20: Transcendental extensions 14E08: Rationality questions [See also 14M20] 20B30: Symmetric groups 20B35: Subgroups of symmetric groups


TSUNOGAI, Hiroshi. Toward Noether's Problem for the Fields of Cross-ratios. Tokyo J. of Math. 39 (2017), no. 3, 901--922. doi:10.3836/tjm/1491465735.

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