Adeles and class fields
| Thesis title in Czech: | Adély a třídová tělesa |
|---|---|
| Thesis title in English: | Adeles and class fields |
| Key words: | adely|idely|třídové těleso|Artinova reciprocita |
| English key words: | adèles|idèles|class field|Artin reciprocity |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 25.02.2023 |
| Date of assignment: | 25.02.2023 |
| Confirmed by Study dept. on: | 15.03.2023 |
| Date and time of defence: | 07.06.2023 09:00 |
| Date of electronic submission: | 02.05.2023 |
| Date of submission of printed version: | 09.05.2023 |
| Date of proceeded defence: | 07.06.2023 |
| Opponents: | Stevan Gajović, Ph.D. |
| Guidelines |
| In the thesis, the student will carefully work out the fundamental properties of adeles and ideles of a number field (in particular, concerning their topology and local compactness). She will also precisely formulate the statements of (global) class field theory, both in the languages of ideals and ideles, explain the relation between them, and illustrate them on suitable examples. |
| References |
| J.W.S. Cassels, A. Fröhlich, Algebraic Number Theory, Thompson Book Company Inc., Washington, D.C. (1967)
H.P.F. Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory, Cambridge University Press, Cambridge (2001) J.S. Milne, Class Field Theory, v4.03 (2020), https://www.jmilne.org/math/CourseNotes/CFT.pdf D. Garbanati, Class field theory summarized, The Rocky Mountain Journal of Mathematics, Vol. 11, No.2 (1981), pp. 195-225, https://www.jstor.org/stable/44236593 |