the graber-harris-starr theorem says that any family of smooth rationally connected varieties over a complex curve has a section. a natural analogue of this statement in mixed characteristic would be that every rationally connected variety over the maximal unramified extension of a p-adic field has a rational point. i will discuss a geometric approach to this problem, as well as a proof of this statement for del pezzo surfaces (for ${p>3}$). this is joint work with david zureick-brown.