Deformation data, Belyi maps, and the local lifting problem
  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 $p$. 
Irene I. Bouw, Stefan Wewers, Leonardo Zapponi