Local-global principles for norm equations

André Macedo (University of Reading)

09-Sep-2020, 00:00-00:30 (4 years ago)

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 developing explicit 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 this 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

number theory

Audience: researchers in the discipline


POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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Organizers: Jessica Fintzen*, Karol Koziol*, Joshua Males*, Aaron Pollack, Manami Roy*, Soumya Sankar*, Ananth Shankar*, Vaidehee Thatte*, Charlotte Ure*
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