André Macedo (Reading) - Explicit methods for the Hasse norm principle
| Dates: | 28 January 2020 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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| Speaker: | André Macedo |
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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.
Speaker
André Macedo
Organisation: University of Reading
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Frank Adams 1
Alan Turing Building
Manchester
