English
Counting S4 and S5 extensions satisfying the Hasse norm principle
Multi angle
Auteurs : Newton, Rachel (Auteur de la Conférence)
CIRM (Editeur )
11R37 - Class field theory
11R45 - Density theorems
14G05 - Rational points
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : Hasse norm principle; number fields; non-abelian extensions
11R37 - Class field theory
11R45 - Density theorems
14G05 - Rational points
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 28/06/2023 Date de captation : 05/06/2023 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 00:55:33 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-05_Newton_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesOrganisateurs de la rencontre : Anni, Samuele ; Bruin, Nils ; Kohel, David ; Martindale, Chloe Dates : 05/06/2023 - 09/06/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2889.html
Données de citation
DOI : 10.24350/CIRM.V.20054603Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] An efficient break of the supersingular isogeny Diffie-Hellman protocol / Auteur de la Conférence Castryck, Wouter.
- [Multi angle] Probabilistic approaches to rational points on algebraic surfaces / Auteur de la Conférence Várilly-Alvarado, Anthony.
- [Multi angle] Isogeny-based cryptography on the (abelian) surface / Auteur de la Conférence Ti, Yan Bo.
- [Multi angle] The geometry of stable lattices in Bruhat-Tits buildings / Auteur de la Conférence Stanojkovski, Mima.
- [Multi angle] Computing Ceresa classes of curves / Auteur de la Conférence Srinivasan, Padmavathi.
Bibliographie
- 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
