Subfields of quaternion algebras in characteristic 2

We discuss the situation where two quaternion algebras over a field of characteristic 2 share the same genus, i.e. have the same set of isomorphism classes of quadratic field extension of the center. We provide examples of pairs of nonisomorphic quaternion algebras who satisfy this property, and show that over global fields and the fields of Laurents series over perfect fields the quaternion algebras are uniquely determined by their maximal subfields.

This talk is based on a joint work with Andrew Dolphin and Ahmed Laghribi.