On the characterization of abelian varieties in characteristic $p>0$

Christopher Hacon, Zsolt Patakfalvi

Published 2016-02-04Version 1

We show that if $X$ is a smooth projective variety over an algebraically closed field of characteristic $p>0$ such that $\kappa (X)=0$ and the Albanese morphism is generically finite with degree not divisible by $p$, then $X$ is birational to an abelian variety. We also treat the cases when $a$ is separable (possibly with degree divisible by $p$) and $A$ is either supersingular or ordinary.