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Mathematics > Algebraic Geometry

arXiv:1812.05018 (math)
[Submitted on 12 Dec 2018]

Title:Review on rationality problems of algebraic k-tori

Authors:Youngjin Bae
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Abstract:Rationality problems of algebraic k-tori are closely related to rationality problems of the invariant field, also known as Noether's Problem. We describe how a function field of algebraic k-tori can be identified as an invariant field under a group action and that a k-tori is rational if and only if its function field is rational over k. We also introduce character group of k-tori and numerical approach to determine rationality of k-tori.
Subjects: Algebraic Geometry (math.AG)
MSC classes: 11E72, 12F20, 13A50, 14E08, 20C10, 20G15
Cite as: arXiv:1812.05018 [math.AG]
  (or arXiv:1812.05018v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.05018

Submission history

From: Youngjin Bae [view email]
[v1] Wed, 12 Dec 2018 16:40:46 UTC (7 KB)
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