Lifting globally $F$-split surfaces to characteristic zero

Abstract

We prove that every globally $F$-split surface admits an equisingular lifting over the ring of Witt vectors.

arXiv commentv3: 53 pages,appeared in Crelle. In Proposition 5.9 we missed a case in the classification of log Calabi--Yau surfaces in in characteristic 2. This is fixed in Proposition 5.11 of 2506.01007