Oort's conjecture on lifting cyclic Galois covers

Let $k$ be an algebraically closed field of characteristic $p$, and let a Galois cover mean a cover of smooth $k$-curves equipped with its finite group of deck transformations. A cover lifts to characteristic zero if it is the closed fiber of a corresponding Galois cover of normal projective curves over a complete discrete valuation ring whose fraction field has characteristic zero and residue field is $k$.

Oort's conjecture. Every cyclic Galois cover of $k$-curves lifts to characteristic zero.

The conjecture is the foundational global lifting question for wildly ramified covers. It was proved by the combined work of Obus and Wewers and of Pop, so every cyclic group is now known to be an Oort group.