Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

15 28

Constructing abelian extensions with prescribed norms

By Christopher Frei

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).

Information about the video

Date of recording 24/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19687303
Cite this video Frei, Christopher (24/11/2020). Constructing abelian extensions with prescribed norms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19687303
URL https://dx.doi.org/10.24350/CIRM.V.19687303

Domain(s)

Number Theory

Bibliography

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

MSC codes

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