Richard Pink: Katalogdaten im Frühjahrssemester 2021 |
| Name | Herr Prof. em. Dr. Richard Pink |
| Lehrgebiet | Mathematik |
| Adresse | Professur für Mathematik ETH Zürich, HG G 65.2 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 06 40 |
| richard.pink@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~pink |
| Departement | Mathematik |
| Beziehung | Professor emeritus |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-4116-12L | Lectures on Drinfeld Modules  | 6 KP | 3V | R. Pink | |
| Kurzbeschreibung | Drinfeld modules: Basic theory, analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations, endomorphism rings, etc. | ||||
| Lernziel | |||||
| Inhalt | A central role in the arithmetic of fields of positive characteristic p is played by the Frobenius map x ---> x^p. The theory of Drinfeld modules exploits this map in a systematic fashion. Drinfeld modules of rank 1 can be viewed as analogues of the multiplicative group and are used in the class field theory of global function fields. Drinfeld modules of arbitrary rank possess a rich theory which has many aspects in common with that of elliptic curves, including analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations. A full understanding of Drinfeld modules requires some knowledge in the arithmetic of function fields and, for comparison, the arithmetic of elliptic curves, which cannot all be presented in the framework of this course. Relevant results from these areas will be presented only cursorily when they are needed, but a fair amount of the theory can be developed without them. | ||||
| Literatur | Drinfeld, V. G.: Elliptic modules (Russian), Mat. Sbornik 94 (1974), 594--627, translated in Math. USSR Sbornik 23 (1974), 561--592. Deligne, P., Husemöller, D: Survey of Drinfeld modules, Contemp. Math. 67, 1987, 25-91. Goss, D.: Basic structures in function field arithmetic. Springer-Verlag, 1996. Drinfeld modules, modular schemes and applications. Proceedings of the workshop held in Alden-Biesen, September 9¿14, 1996. Edited by E.-U. Gekeler, M. van der Put, M. Reversat and J. Van Geel. World Scientific Publishing Co., Inc., River Edge, NJ, 1997. Thakur, Dinesh S.: Function field arithmetic. World Scientific Publishing Co., Inc., River Edge, NJ, 2004. Further literature will be indicated during the course | ||||
| 401-5110-00L | Number Theory Seminar | 0 KP | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |
| Kurzbeschreibung | Forschungskolloquium | ||||
| Lernziel | Vorträge über neue Themen aus der Forschung. | ||||
| Inhalt | Forschungsseminar in Algebra, Zahlentheorie und Geometrie, richtet sich insbesondere an Mitarbeiterinnen und Mitarbeiter sowie Doktorandinnen und Doktoranden. | ||||