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SUMMARY:S_n-extensions with prescribed norms - Sebastian Monnet (UCL)
DTSTART:20250128T143000Z
DTEND:20250128T153000Z
UID:TALK225649@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Let α be a rational number and let Σ be a family of number f
 ields.  For each number field K in Σ\, either α is a norm of K\, or it i
 s 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} w
 as solved by Frei\, Loughran\, and Newton.  We will discuss new results fo
 r the simplest class of nonabelian extensions: so-called "generic" number 
 fields of a given degree.
LOCATION:MR13
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