##### Department of Mathematics,

University of California San Diego

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### Math 208 - Seminar in Algebraic Geometry

## Iacopo Brivio

#### National Center for Theoretical Sciences

## Lifting globally F-split surfaces to characteristic zero

##### Abstract:

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

### October 14, 2022

### 4:00 PM

Email Jacob Keller (jjkeller@ucsd.edu)

for the Zoom link

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