Local Oort groups and the isolated differential data criterion

Abstract

It is conjectured that if k is an algebraically closed field of characteristic p>0, then any branched G-cover of smooth projective k-curves where the “KGB” obstruction vanishes and where a p-Sylow subgroup of G is cyclic lifts to characteristic 0. Obus has shown that this conjecture holds given the existence of certain meromorphic differential forms on ℙ k 1 with behavior determined by the ramification data of the cover. We give a more efficient procedure to compute these forms than was previously known. As a consequence, we show that all D 25 -covers and D 27 -covers lift to characteristic zero.