3 problems

Oort conjecture revisited. Local cyclic extensions are liftable in towers: given the local $G$-extension $k[[z]]/k[[t]]$ and a characteristic-zero lift $R[[S]]/R[[T]]$ of a subexte…

Dihedral weak local Oort conjecture. The group $D_{2^n}$ is a weak local Oort group for $2$.

KGB obstruction conjecture. The KGB obstruction is the only obstruction to the local lifting problem for local $G$-extensions where $G$ has cyclic $p$-Sylow subgroup. In particular…