A variety $X$ over an algebraically closed field $k$ of characteristic $p>0$ is Witt-liftable if it is the closed fiber of a flat morphism $\mathcal{X}\to\mathrm{Spec}W(k)$, where $W(k)$ denotes the ring of Witt vectors of $k$. The existence of such a lift allows us to study $X$ using techniques from complex geometry. Although it is well-known that such a lift does not always exist, it is conjectured that every globally F-split variety is Witt-liftable. We show a stronger result in dimension two, and apply this to the study of singularities of globally F-split del Pezzo and Calabi-Yau surfaces. This is a joint work with F. Bernasconi, T. Kawakami, and J. Witaszek.

Pre-talk: 3:30-4:00pm