Prof. Dr. Gubler

Diophantine Geometry is a very old and fascinating field. It deals with entire or rational
solutions of polynomial equations. A famous example is Fermat's conjecture which was open for many
years until Wiles solved it recently. In Diophantine Geometry I, we will introduce heights and we
will prove Roth's theorem from diophantine approximation and the theorem of Mordell-Weil from the
theory of abelian varieties. In diophantine geometry II, these two theorems lead to a proof of the
Mordell-conjecture. We will follow Vojta's proof with simplification of Bombieri. This proof is
more elementary than the original proof of Faltings for which Faltings received the Fields medal in
1986.

An introduction to algebraic geometry with an emphasis on quasiprojective varieties over a field.

Übungseinteilung