The Hurwitz tree obstruction for the refined local lifting problem

Abstract

We prove that the differential Hurwitz tree obstruction for the cyclic $p$-power refined local lifting problem always vanishes. Given a cyclic extension of degree $p^n$ in characteristic $p$ and a lift of its degree-$p^{n-1}$ subextension, we construct a compatible differential Hurwitz tree extending the tree of that lift. Realizing the resulting tree by a cover remains a separate problem.

Substantially revised; proves that the differential Hurwitz tree obstruction always vanishes for cyclic $p$-power covers