Lifting globally $F$-split surfaces to characteristic zero

TL;DR

This paper proves that all globally F-split surfaces can be lifted to characteristic zero in an equisingular manner over Witt vectors, bridging positive characteristic geometry with characteristic zero.

Contribution

It establishes a universal lifting result for globally F-split surfaces, a significant advancement in understanding their deformation theory.

Findings

Every globally F-split surface admits an equisingular lifting.

Lifting is achieved over the ring of Witt vectors.

The result connects positive characteristic geometry with characteristic zero.

Abstract

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