Spherical Roots of Spherical Varieties in Characteristic 2

The embeddings of a spherical homogeneous space G/H are classified using G-invariant valuations of the function field. These can be seen in a certain Q-vector space where they form a cone. Michel Brion proved that in characteristic zero this is an antidominant fundamental domain for a finite reflection group generated by the so-called spherical roots of the variety. This was recently generalized by Friedrich Knop to odd characteristics. After giving an introduction to the embedding theory I will present interesting counterexamples in characteristic two.