M/E23

In this talk I will look at different fields where one has (or might hope for) a local-global principle for isotropy with respect to a certain set of valuations. For 4-dimensional quadratic forms this problem is closely related to quaternion algebras and their quadratic subfields. I will give some examples over rational function fields. When a local-global principle holds over some field, I will indicate how this can be used to obtain first-order definitions for certain integrally closed subrings.

Karim Becher

Universiteit Antwerpen