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