Markus Rost
Institute for Advanced Study and the University of Bielefeld

Examples in Algebraic Cobordism

Characteristic numbers of differentiable or complex manifolds play an important role in the classical theory of cobordism. In recent years there appeared a surprising relation between this topic and Galois cohomology. It turned out that characteristic numbers give rise to certain birational invariants which are of particular interest over non-algebraically closed fields. In the lecture we will consider various examples which illustrate this new appearance of characteristic numbers in questions from algebra and algebraic geometry.