André Macedo (Reading) - Explicit methods for the Hasse norm principle
|Starts:||15:00 28 Jan 2020|
|Ends:||16:00 28 Jan 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Adults, Alumni, Current University students|
Abstract: Given 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 everywhere locally is in fact a global norm from L. If L/K is cyclic, the original Hasse norm theorem states that the HNP holds. More generally, there is a cohomological description (due to Tate) of the obstruction to the HNP for Galois extensions.
In this talk, I will present work (joint with Rachel Newton) developing explicit methods to study this principle for non-Galois extensions. As a key application, I will describe how these methods can be used to characterize the HNP for extensions whose normal closure has Galois group A_n or S_n. I will additionally discuss the geometric interpretation of this principle and how it relates to the weak approximation property for norm one tori. If time permits, I will also present some recent generalizations of the aforementioned methods to study the Hasse principle for multinorm equations.
Organisation: University of Reading
Travel and Contact Information
Frank Adams 1
Alan Turing Building