242582 Fortgeschrittene Themen der algebraischen Zahlentheorie (VÜA) (SoSe 2021)
Contents, comment
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In diesem modulartiger Kurs werden einige fortgeschrittene Themen der algebraischen Zahlentheorie behandelt, darunter Kreisteilungskörper, Klassenkörpertheorie, die Theorie der komplexen Multiplikation, und die Theorie der Heckeschen L-Funktionen (d'après Tate), die durch die Arithmetik von Shimura-Kurven motiviert sind. In der zweiten Hälfte des Kurses wird die Theorie der modularen Kurven und Shimura-Kurven entwickelt.
Bibliography
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D.Bump, Automorphic Forms and Representations, Cambridge Stud. Adv. Math. 55, Cambridge University Press (1998).
L. Washington, Cyclotomic Fields (Second Edition), Springer GTM 83 (1982).
J. Neukirch, Algebraische Zahlentheorie, Springer-Verlag Berlin (1992).
J.-P. Serre, “Complex Multiplication”, in ``Algebraic Number Theory" (Second Edition), Eds. J.W.S. Cassels and A. Fröhlich, London Math. Soc. (2010), 292-296.
J. Tate, “Fourier Analysis in Number Fields and Hecke's Zeta Functions”, ibid., 305-347.
K. Ribet and W. Stein, Lectures on modular forms and Hecke operators.
H. Carayol, Sur la mauvaise réduction des courbes de Shimura, Compos. Math. 59 (1986).
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| Frequency | Weekday | Time | Format / Place | Period |
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| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-P1a Profilierung 1 Teil A | Profilierungsvorlesung (mit Übung) - Typ 2 | Study requirement
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| 24-M-P1b Profilierung 1 Teil B | Profilierungsvorlesung (mit Übung) - Typ 2 | Study requirement
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| 24-M-P2 Profilierung 2 | Profilierungsvorlesung (mit Übungen) - Typ 2 | Study requirement
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