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Class field theory - Lecture 1
Multi angle
Authors : Stevenhagen, Peter (Author of the conference)
CIRM (Publisher )
11R18 - Cyclotomic extensions
11R37 - Class field theory
11R45 - Density theorems
CIRM (Publisher )
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Abstract :
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.
Keywords : Class field theory
MSC Codes : 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.
Keywords : Class field theory
11R18 - Cyclotomic extensions
11R37 - Class field theory
11R45 - Density theorems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/05/2023 Conference Date : 08/05/2023 Subseries : Research School arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 01:07:00 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-08_StevenHagen.mp4 
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Information on the Event
Event Title : Jean Morlet Chair - Spring School in Arithmetic Statistics / Chaire Jean Morlet - École de statistiques arithmétiquesEvent Organizers : Stevenhagen, Peter ; Anni, Samuele ; Rosu, Eugenia ; Coppola, Nirvana ; Pengo, Riccardo Dates : 08/05/2023 - 12/05/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2679.html
Citation Data
DOI : 10.24350/CIRM.V.20042303Cite this video as: 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 |
See Also
- [Multi angle] Galois representations and statistics - Lecture 1 / Author of the conference Schoof, René.
- [Multi angle] Frobenius distributions - Lecture 1 / Author of the conference Kedlaya, Kiran.
- [Multi angle] Complex multiplication - Lecture 1 / Author of the conference Vonk, Jan.
Bibliography
- 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
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