Topics in group schemes and surfaces in positive characteristic

Nikolaos Tziolas

Published 2024-04-03Version 1

This is a survey paper on algebraic surfaces in positive characteristic based on a series of lectures that the author gave at the University of Edinburgh in March 2023. It is focused on certain positive characteristic phenomena like infinitesimal group schemes and their actions on algebraic surfaces as well as the failure in positive characteristic of certain fundamental characteristic zero results like the Kodaira vanishing theorem. Many explicit examples are presented.