%0 Journal Article %T Deformation data, Belyi maps, and the local lifting problem %A Irene I. Bouw %A Stefan Wewers %A Leonardo Zapponi %J Mathematics %D 2008 %I arXiv %X We prove existence and nonexistence results for certain differential forms in positive characteristic, called {\em good deformation data}. Some of these results are obtained by reduction modulo $p$ of Belyi maps. As an application, we solve the local lifting problem for groups with Sylow $p$-subgroup of order $p$. %U http://arxiv.org/abs/0801.1418v1