WiSe 14/15: Proseminar/Seminar p-adische Zahlen
Hélène Esnault
Zusätzl. Angaben / Voraussetzungen
Prerequistes:
1) very basic knowledge about algebra and topology, for example the notion of field, ring, topological space.
2) a certain familiarity with undergraduate level analysis, for example the notion continuous functions, convergent sequences, power series.
Kommentar
In the Proseminar we will first discuss the basics of p-adic numbers - the topology and the algebraic structure, the metrics etc., then we will do analysis on p-adic numbers like we did for the fields of real numbers and complex numbers, the students should see a strong analogy between p-adic numbers and the classical real and complex numbers at this point. In the end we will discuss a few deeper topics, possibilities are:
1) the completion of the algebraic closure of the p-adic numbers;
2) p-adic interpolation of the Riemann zeta-function.
References: 1) p-adic numbers, Fernando Q. Gouvea, Springer-Verlag, 1993.
2) p-adic numbers, p-adic analysis, and zeta-functions, Neal Koblitz, GTM 58.
We will meet on October 13th, 2014 at 2:00 pm to discuss about the topics. If you have some other suggestions or questions, please contact me via l.zhang@fu-berlin.de. Hope to see you soon!
16 Termine
Regelmäßige Termine der Lehrveranstaltung