Explicit Sarkisov program for regular surfaces over arbitrary fields and applications

We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields of characteristic p>0. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, generalising work of Iskovskikh. As an application, we discuss rationality problems for regular surfaces and the structure of the plane Cremona group.
Comment: 71 pages. Expanded the section on existence of Sarkisov links, added theorem that over separably closed fields of characteristic distinct from two, the plane Cremona group is generated by involutions