Noether's problem and rationality problem for multiplicative invariant fields: a survey
Akinari Hoshi
TL;DR
This survey reviews recent advances in Noether's problem and the rationality problem for multiplicative invariant fields, highlighting key results over Q and C, and summarizing various authors' contributions.
Contribution
It compiles and discusses recent developments and results related to Noether's problem and rationality issues for multiplicative invariant fields.
Findings
Progress on Noether's problem over Q and C.
New criteria for rationality of multiplicative invariant fields.
Summary of key results from recent papers.
Abstract
In this paper, we give a brief survey of recent developments on Noether's problem and rationality problem for multiplicative invariant fields including author's recent papers Hoshi [Hos15] about Noether's problem over Q, Hoshi, Kang and Kunyavskii [HKK13], Chu, Hoshi, Hu and Kang [CHHK15], Hoshi [Hos16] and Hoshi, Kang and Yamasaki [HKY16] about Noether's problem over C, and Hoshi, Kang and Kitayama [HKK14] and Hoshi, Kang and Yamasaki [HKY] about rationality problem for multiplicative invariant fields.
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Taxonomy
TopicsFinite Group Theory Research · Algebraic Geometry and Number Theory · Coding theory and cryptography