Stability conditions under change of base field

We investigate the behaviour of Bridgeland stability conditions under change of base field with particular focus on the case of finite Galois extensions. In particular, we prove that for a variety X over a field K and a finite Galois extension L/K the stability manifold of X embeds as a closed submanifold into the stability manifold of the base change variety.
Comment: 18 pages; v2: minor revision