An Enriques Classification Theorem for Surfaces in Positive Characteristic

Abstract

We prove that a smooth projective surface $S$ over an algebraically closed field of characteristic $p>3$ is birational to an abelian surface if $P_1(S)=P_4(S)=1$ and $h^1(S,{\mathcal{O}}_S)=2$.

Minor changes to the previous version: misprints corrected