The study of solutions of polynomial equations is one of the most fundamental tasks of algebra and algebraic geometry. Arithmetic comes into play when the coefficients and solutions of the equation are restricted for example to the integers (the most famous example being Fermat´s Last Theorem). Local-global principles are an important tool for investigating such arithmetic questions, as they reduce the problem at hand to a set of problems that are (potentially) easier to handle.

In this talk, we give some classical examples of local-global principles and how they can be phrased in terms of Galois cohomology. We then consider analogous situations over so-called arithmetic function fields, where the geometry of the underlying curve can be used to obtain new results.

No prior knowledge of Galois cohomology is assumed in the talk.

[UPDATE] Download video of this colloquium at http://media.sas.upenn.edu/math/Colloquia2012/Hartmann10- 24-12.MOV