This book represents the current (1985) state of knowledge about Zariski surfaces and related topics in differential equations in characteristic p > 0. It is aimed at research mathematicians and graduate and advanced undergraduate students of mathematics and computer science.
Table of Contents
Introduction 1. Basic Theory of Zariski Surfaces 2. Links with Differential Equations in Characteristic p > 0 3. The Divisor Classes of the Surface zpn = G(x,y) 4. Picard Groups of Generic Zariski Surfaces 5. The Divisor Classes of zp = G(x,y): A Programmable Problem 6. Families of Zariski Surfaces 7. Unirationality of Enriques Surfaces in Characteristic 2 8. Applications of the de Rham-Witt Complex and of Dominoes to Zariski Surfaces 9. Picard and Brauer Groups of Zariski Surfaces 10. A Counterexample to Zariski's Problem and an Example of a Surface with Nonreduced Picard Scheme