University of Georgia
Mathematics Department Colloquium
Prof. Dr. Hans Peter Schlickewei
Philipps-Universitaet Marburg
December 2, 1999
The Subspace Theorem in Diophantine Approximations
Abstract: The famous theorem of Roth says the following:
Suppose $\alpha$ is an algebraic number and $\epsilon > 0$.
Then the inequality $|\alpha - x/y| < y^{-2-epsilon}$ has only
finitely many rational solutions $x/y$.
The Subspace Theorem of W.M.Schmidt generalizes this to
arbitrary dimensions. In recent years there has been a dramatic
development in that area. Quantitative versions of the Subspace
Theorem have been given, that have allowed it to prove some old
conjectures on the number of solutions of certain diophantine equations.
I will give a survey on these developments and in particular explain
the most general result on the Subspace Theorem proved in collaboration
with J.H. Evertse.