Algebraic Surfaces in Positive Characteristic

TL;DR

This paper provides an introduction and overview of algebraic surfaces over algebraically closed fields of positive characteristic, covering classification, special topics, and applications to characteristic zero.

Contribution

It offers a comprehensive survey of algebraic surfaces in positive characteristic, including classification and lifting results, with connections to complex geometry.

Findings

Sketches the Kodaira-Enriques classification in positive characteristic

Discusses special characteristic-p topics and lifting results

Provides applications to characteristic zero geometry

Abstract

These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira-Enriques classification. Next, we turn to more special characteristic-p topics, and end by lifting results and applications to characteristic zero. We assume that the reader has a background in complex geometry and has seen the Kodaira-Enriques classification of complex surfaces before.