Cyclic Sylow lifting conjecture

Let $G$ be a finite group with a cyclic $p$-Sylow subgroup, and let $k[[z]]/k[[t]]$ be a $G$-extension. Cyclic Sylow lifting conjecture. For every such extension, the KGB obstruction is the only obstruction to lifting. The paper places this among open problems concerning local Oort groups and lifting of local extensions.