Local Oort groups and the isolated differential data criterion

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 P1 k 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.