English
Class field theory - Lecture 1
Multi angle
Auteurs : Stevenhagen, Peter (Auteur de la conférence)
CIRM (Editeur )
11R18 - Cyclotomic extensions
11R37 - Class field theory
11R45 - Density theorems
CIRM (Editeur )
Loading the player...
|
Résumé :
This is the introductory lecture of the course on class field theory in the Research school on Arithmetic Statistics in May 2023. It briefly reviews the necessary algebraic number theory, and presents class field theory as the analogue of the Kronecker-Weber theorem over number fields. In a similar way, the Chebotarev density theorem is treated as an analogue of the Dirichlet theorem on primes in arithmetic progressions.
Two further lectures dealt with idelic and cohomological reformulations of the main theorem of class field theory, and two more were devoted to power reciprocity laws and Redei reciprocity.
Mots-Clés : Class field theory
Codes MSC : Two further lectures dealt with idelic and cohomological reformulations of the main theorem of class field theory, and two more were devoted to power reciprocity laws and Redei reciprocity.
Mots-Clés : Class field theory
11R18 - Cyclotomic extensions
11R37 - Class field theory
11R45 - Density theorems
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 22/05/2023 Date de Captation : 08/05/2023 Sous Collection : Research School Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 01:07:00 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-08_StevenHagen.mp4 
|
Informations sur la Rencontre
Nom de la Rencontre : Jean Morlet Chair - Spring School in Arithmetic Statistics / Chaire Jean Morlet - École de statistiques arithmétiquesOrganisateurs de la Rencontre : Stevenhagen, Peter ; Anni, Samuele ; Rosu, Eugenia ; Coppola, Nirvana ; Pengo, Riccardo Dates : 08/05/2023 - 12/05/2023 Année de la rencontre : 2023 URL de la Rencontre : https://conferences.cirm-math.fr/2679.html
Données de citation
DOI : 10.24350/CIRM.V.20042303Citer cette vidéo: Stevenhagen, Peter (2023). Class field theory - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20042303 URI : http://dx.doi.org/10.24350/CIRM.V.20042303 |
Voir Aussi
- [Multi angle] Galois representations and statistics - Lecture 1 / Auteur de la conférence Schoof, René.
- [Multi angle] Frobenius distributions - Lecture 1 / Auteur de la conférence Kedlaya, Kiran.
- [Multi angle] Complex multiplication - Lecture 1 / Auteur de la conférence Vonk, Jan.
Bibliographie
- COHEN, H. . Computational Class Field Theory. In: Advanced Topics in Computational Number Theory. Graduate Texts in Mathematics, vol 193. Springer, New York, NY 2000 - https://doi.org/10.1007/978-1-4419-8489-0_4
- STEVENHAGEN, Peter. The arithmetic of number rings. Algorithmic number theory: lattices, number fields, curves and cryptography, 2008, vol. 44, p. 209-266. - http://library.msri.org/books/Book44/files/08psh.pdf
- STEVENHAGEN, Peter. Redei reciprocity, governing fields and negative Pell. In : Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 2022. p. 627-654. - https://doi.org/10.1017/S0305004121000335
Imagette Video
