S_n-extensions with prescribed norms

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• Sebastian Monnet (UCL)
• Tuesday 28 January 2025, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

Let α be a rational number and let Σ be a family of number fields. For each number field K in Σ, either α is a norm of K, or it is not. We might ask for what proportion of K in Σ this is the case. We will see that this is a natural question to ask, and that it is extremely hard in general. For an abelian group A, the case Σ = {A-extensions} was solved by Frei, Loughran, and Newton. We will discuss new results for the simplest class of nonabelian extensions: so-called “generic” number fields of a given degree.

This talk is part of the Number Theory Seminar series.

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