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Ekedahl wrote about foliations in positive characteristic, over the field $\mathbb{Z}/p\mathbb{Z}$ as a subsheaf of the tangent sheaf, that are closed with respect to involution and $p$-power.

My question is: does there exist a reference about this theory but over the ring $\mathbb{Z}/p^{n}\mathbb{Z}$?

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Do you really mean the ring $\mathbb{Z}/p^{n}\mathbb{Z}$ or maybe the finite field $\mathbb{F}_{p^n}$ which is a field extension of $\mathbb{F}_p=\mathbb{Z}/p\mathbb{Z}$ ? If you do mean the first, what are some of your motivations? By the way, I think foliation theory can be defined over any field of positive characteristic as well. – Qfwfq Nov 19 '12 at 14:33
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Look at this paper: Miyaoka, Yoichi(J-TOKYM) Deformations of a morphism along a foliation and applications. Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 245–268, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987. – Sándor Kovács Nov 19 '12 at 16:50

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