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SUMMARY:André Macedo (University of Reading)
DTSTART:20200909T000000Z
DTEND:20200909T003000Z
DTSTAMP:20260423T035728Z
UID:POINT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/7/">Lo
 cal-global principles for norm equations</a>\nby André Macedo (University
  of Reading) as part of POINT: New Developments in Number Theory\n\n\nAbst
 ract\nGiven an extension L/K of number fields\, we say that the Hasse norm
  principle (HNP) holds if every non-zero element of K which is a norm ever
 ywhere locally is in fact a global norm from L. If L/K is cyclic\, the ori
 ginal Hasse norm theorem states that the HNP holds. More generally\, there
  is a cohomological description (due to Tate) of the obstruction to the HN
 P for Galois extensions. In this talk\, I will present work developing exp
 licit methods to study this principle for non-Galois extensions as well as
  some key applications in extensions whose normal closure has Galois group
  A_n or S_n. I will additionally discuss the geometric interpretation of t
 his concept and how it relates to the weak approximation property for norm
  varieties. If time permits\, I will also present some recent developments
  on the statistics of the HNP\n
LOCATION:https://researchseminars.org/talk/POINT/7/
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