Prof. Dr. Jens Franke

Sprechstunden

Freitags, von 14.20 bis 15.20, in meinem Büro (1.026).

Lectures "Mordell-Weil and Faltings-Mordell" and "Rigid analytic and adic spaces"

I intend to offer two advanced lectures this term. The first one is on rational points and will give proofs of the Mordell-Weil theorem on rational points on abelian varieties and of Faltings' theorem establishing the Mordell conjecture in the number field case: Any curve of genus larger than one has but finitely many rational points. The proof of Faltings-Mordell will be Vojta's with the simplifications by Bombieri, although our presentation well be somewhere in the middle between these two papers. Prerequisites for this lecture are a knowledge of schemes, abelian varieties, and Jacobians of curves. This lecture has been scheduled for Monday and Friday 14.15-15.45 in N0.008.

The other lecture introduces rigid analytic and adic spaces and the relation between both notions. An introduction to the cohomology of sheaves of modules over the structure sheaf will be given. Etale cohomology will not be covered, however. A good knowledge of schemes and the cohomology of sheaves of modules on schemes, as well as of the basic theory of local fields, is absolutely necessary. Apart from this I hope to be able to adapt the lecture to the background of the audience. This lecture has been scheduled for Tuesday and Friday 12.15-13.45 in N0.008.

Seminar "Geometrische Konstruktionen und transzendente Zahlen."

Das Seminar fand im Sommersemester 2016 für Studenten des zweiten Semesters statt. Um einen guten Anschluß an die Vorlesung "Lineare Algebra I" sicherzustellen, diente ein von mir selbst verfaßter Text als Grundlage des Seminares. Dieser soll hier weiterhin zur Verfüfung gestellt werden.

Vorlesungen "Mathematik für Physiker I-III"

Die Javascript-Programme zu den Anwesenheitsübungen dieser Vorlesungen, die ich zwischen 2008 und 2011 gehalten habe, sind weiterhin online:

Selected Publications