Français
Counting S4 and S5 extensions satisfying the Hasse norm principle
Multi angle
Authors : Newton, Rachel (Author of the conference)
CIRM (Publisher )
11R37 - Class field theory
11R45 - Density theorems
14G05 - Rational points
CIRM (Publisher )
Loading the player...
|
Abstract :
Let $L/K$ be an extension of number fields. The norm map $N_{L/K} :L^{*}\to K^{*}$ extends to a norm map from the ideles of L to those of $K$. The Hasse norm principle is said to hold for $L/K$ if, for elements of $K^{*}$, being in the image of the idelic norm map is equivalent to being the norm of an element of L^{*}. The frequency of failure of the Hasse norm principle in families of abelian extensions is fairly well understood, thanks to previous work of Christopher Frei, Daniel Loughran and myself, as well as recent work of Peter Koymans and Nick Rome. In this talk, I will focus on the non-abelian setting and discuss joint work with Ila Varma on the statistics of the Hasse norm principle in field extensions with normal closure having Galois group $S_{4}$ or $S_{5}$.
Keywords : Hasse norm principle; number fields; non-abelian extensions
MSC Codes : Keywords : Hasse norm principle; number fields; non-abelian extensions
11R37 - Class field theory
11R45 - Density theorems
14G05 - Rational points
|
Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 28/06/2023 Conference Date : 05/06/2023 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:55:33 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-05_Newton_1.mp4 
|
Information on the Event
Event Title : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesEvent Organizers : Anni, Samuele ; Bruin, Nils ; Kohel, David ; Martindale, Chloe Dates : 05/06/2023 - 09/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2889.html
Citation Data
DOI : 10.24350/CIRM.V.20054603Cite this video as: Newton, Rachel (2023). Counting S4 and S5 extensions satisfying the Hasse norm principle. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20054603 URI : http://dx.doi.org/10.24350/CIRM.V.20054603 |
See Also
- [Multi angle] An efficient break of the supersingular isogeny Diffie-Hellman protocol / Author of the conference Castryck, Wouter.
- [Multi angle] Probabilistic approaches to rational points on algebraic surfaces / Author of the conference Várilly-Alvarado, Anthony.
- [Multi angle] Isogeny-based cryptography on the (abelian) surface / Author of the conference Ti, Yan Bo.
- [Multi angle] The geometry of stable lattices in Bruhat-Tits buildings / Author of the conference Stanojkovski, Mima.
- [Multi angle] Computing Ceresa classes of curves / Author of the conference Srinivasan, Padmavathi.
Bibliography
- FREI, Christopher, LOUGHRAN, Daniel, et NEWTON, Rachel. The Hasse norm principle for abelian extensions. American Journal of Mathematics, 2018, vol. 140, no 6, p. 1639-1685. - https://doi.org/10.1353/ajm.2018.0048
- FREI, Christopher, LOUGHRAN, Daniel, et NEWTON, Rachel. Number fields with prescribed norms. Commentarii Mathematici Helvetici, 2022, vol. 97, no 1. - https://doi.org/10.4171/cmh/528
- KOYMANS, Peter et ROME, Nick. A note on the Hasse norm principle. arXiv preprint arXiv:2301.10136, 2023. - https://doi.org/10.48550/arXiv.2301.10136
- KOYMANS, Peter et ROME, Nick. Weak approximation on the norm one torus. arXiv preprint arXiv:2211.05911, 2022. - https://doi.org/10.48550/arXiv.2211.05911
- MACEDO, André et NEWTON, Rachel. Explicit methods for the Hasse norm principle and applications to An and Sn extensions. In : Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 2022. p. 489-529. - https://doi.org/10.1017/S0305004121000268
- ROME, Nick. The Hasse norm principle for biquadratic extensions. Journal de théorie des nombres de Bordeaux, 2018, vol. 30, no 3, p. 947-964. - https://doi.org/10.5802/jtnb.1058
- NEWTON, Rachel et VARMA, Ila. Counting $S_4$ and $S_5$ extensions satisfying the Hasse norm principle. in Progress. -
Imagette Video
