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Sebastian Monnet (UCL)
Tuesday 28 January 2025, 14:30-15:30
S_n-extensions with prescribed norms
- 👤 Speaker: Sebastian Monnet (UCL)
- 📅 Date & Time: Tuesday 28 January 2025, 14:30 - 15:30
- 📍 Venue: MR13
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Rong Zhou
Abstract
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.
Series This talk is part of the Number Theory Seminar series.
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