Foliations on abelian surfaces in positive characteristic

Source abstract

This paper studies foliations on abelian surfaces in positive characteristic. We provide an explicit description of all smooth foliations, linear and turbulent, and establish criteria for being $p$-closed. We explicitly determine the moduli spaces of such foliations. We give an application to the construction of $p$-closed foliations, with mild singularities, on Kummer $K3$-surfaces in positive characteristics.