Noether's problem and descent
Fedor Bogomolov, Yuri Tschinkel
TL;DR
This paper explores Noether's problem through the lens of torsors under linear algebraic groups and descent theory, aiming to understand the rationality of fields fixed under group actions.
Contribution
It introduces a new approach to Noether's problem using torsors and descent, providing insights into the rationality questions for algebraic group actions.
Findings
Established connections between torsors and rationality problems
Provided criteria for the rationality of fixed fields under group actions
Extended the understanding of Noether's problem in algebraic geometry
Abstract
We study Noether's problem from the perspective of torsors under linear algebraic groups and descent.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research