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Audiovisual Mathematics Library

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Virtualconference

Authors : Frei, Christopher (Author of the conference)
CIRM (Publisher )

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Abstract : Let $K$ be a number field, $\alpha _1,...,\alpha _t \in K$ and $G$ a finite abelian group. We explain how to construct explicitly a normal extension $L$ of $K$ with Galois group $G$, such that all of the elements $\alpha_{i}$ are norms of elements of $L$. The construction is based on class field theory and a recent formulation of Tate's criterion for the validity of the Hasse norm principle. This is joint work with Rodolphe Richard (UCL).

Keywords : norm form equations; class field theory

MSC Codes :
11D57 - Multiplicative and norm form equations
11R37 - Class field theory
11Y40 - Algebraic number theory computations
14G05 - Rational points

Information on the Video

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-11-24_Frei.mp4

Information on the Event

Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire
Event Organizers : Rivat, Joël ; Tichy, Robert
Dates : 23/11/2020 - 27/11/2020
Event Year : 2020
Event URL : https://www.chairejeanmorlet.com/2256.html

Citation Data

DOI : 10.24350/CIRM.V.19687303
Cite this video as: Frei, Christopher (2020). Constructing abelian extensions with prescribed norms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19687303
URI : http://dx.doi.org/10.24350/CIRM.V.19687303

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Bibliography

FREI, Christopher et RICHARD, Rodolphe. Constructing abelian extensions with prescribed norms. arXiv preprint arXiv:2006.08968, 2020. - https://arxiv.org/abs/2006.08968

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