| Abstract: | Letk be an algebraically closed field of characteristicp>0 andR be a suitable valuation ring of characteristic 0, dominating the Witt vectorsW(k). We show how Lubin-Tate formal groups can be used to lift those orderp n automorphisms ofk[[Z]] toR[[Z]], which occur as endomorphisms of a formal group overk of suitable height. We apply this result to prove the existence of smooth liftings of galois covers of smooth curves from characteristicp to characteristic 0, provided thep-part of the inertia groups acting on the completion of the local rings at the points of the cover overk arep-power cyclic and determined by an endomorphism of a suitable formal group overk. The author would like to express his thanks to the Max-Planck-Institut für Mathematik, Bonn, for its hospitality and support, where this research was done during a visit from June – September 2001. |
